If the lengths of two altitudes of a triangle are 10 and 15 cm, then which of the following is the range of the third altitude?

△ABC is such that AB = 5 cm, BC = 4 cm and CA = 4.5 cm. △XYZ is similar to △ABC. If YZ = 8 cm, then find the perimeter of △XYZ.

Point M and N are on the sides PQ and QR respectively of a triangle PQR, right angled at Q. If PN = 9 cm, MR = 7 cm and MN = 3 cm, then find the length of PR (in cm).

AB is parallel to DC in a trapezium ABCD. It is given that AB > DC and the diagonals AC and BD intersect at O. If AO = 3x – 15, OB = x + 9, OC = x - 5 and OD = 5, and x has two values x₁ and x₂, then the value of (x₁² + x₂²) is:

ABC is a triangle with sides AB = 41 cm, BC = 28 cm, and CA = 15 cm. If D, E, and F are the midpoints of AB, BC, and CA, respectively, then what is the area of the triangle DEF?

In a parallelogram ABCD, the length of the line joining the midpoints of AD and AC is 2 units. If the perimeter of the parallelogram is 26 units, then find the length of AD.

ABC is an equilateral triangle, P, Q, and R are the midpoints of sides AB, BC, and CA, respectively. If the length of the side of the triangle ABC is 8 cm, then the area of △PQR is:

'O' is a point inside an equilateral triangle. The perpendicular distances from 'O' to the sides are √3 cm, 2√3 cm, and 5√3 cm. The perimeter of the triangle is ..........

In a triangle ABC, AC = 8.4 cm and BC = 14 cm, P is a point on AB such that CP = 11.2 cm and ÐACP = ÐB. What is the length (in cm) of BP?

in triangle STU, V is a point on the side ST and W is a point on the side SU such that VWUT is a trapezium. Given that VW : TU= 2 : 7, what is the ratio of area of trapezium VWUT to the area of the triangle STU?

X, Y, and Z are three equilateral triangles. The sum of the areas of X and Y is equal to the area of Z. If the side lengths of X and Y are 6 cm and 8 cm, respectively, then what is the length of Z?

The areas of the two similar triangles are 225 cm² and 196 cm². If the largest side of the larger triangle is 30 cm, then the longest side of the smaller triangle is:

In \(\triangle\)ABE, D and C are the points on sides AE and EB, respectively, such that DC II AB. If AD = 4 cm, BC = 5 cm, DC = 10 cm, and AB = 15 cm, then the sum of the lengths of DE and EC is:

In ΔPQR, the length of the side QR is less than twice the length of the side PQ by 3 cm. Length of the side PR exceeds the length of the side PQ by 14 cm. The perimeter is 55 cm. The length of the smaller side of the triangle PQR is:

In the following figure, AN = 7 cm, BN = 8 cm, AC = 18 cm. What is the length of BC?

In the figure given below, the lengths of sides AB, BC, and AC of the triangle ABC are 4 cm, 8 cm, and 6 cm respectively. If AD is the median of the triangle and G is the centroid, then what is the length of DG (in cm)?

In the given figure, BE, AD and EF are perpendiculars on sides AC and BC. If AD = 8 cm, AC = 12 cm and BE = 6 cm, then find the length of BC.

In △ABC, ∠B = 87° and ∠C = 60°. Points D and E are on the side AB and AC, respectively, such that ∠DEC = 93° and DE : BC = 5 : 9. If AB = 14.4 cm, then the length of AE is:

R and S are the midpoints of the sides XY and XZ, respectively, of ∆XYZ. Also, XR = 15 cm, XY = 25 cm, XS = 12 cm and XZ = 20 cm. RS is equal to:

In the given figure, ABCDEF is a regular hexagon of side 16 cm. P, Q and R are the midpoints of the sides AB, CD, and EF respectively. What is the area (in cm²) of triangle PQR?

If \(\triangle\)ABC, D is the midpoint of AC, F is a point on AB such that CF bisects BD at E. IF AF = 18 cm, then the length of BF is:

In ΔABC, AB = 20 cm, BC = 7 cm, and AC = 15 cm. Side BC is produced to D such that ΔDAB ~ ΔDCA. The length of the CD is:

In a parallelogram, one of the parallel sides is 16 cm and the other side is 12 cm. If the perpendicular distance between the two parallel sides of dimension 16 cm is 24 cm, then the perpendicular distance between its other two parallel sides is :

In the given fig. ABCD is a trapezium such that AB II CD. NC = 6 cm, AB = 10 cm and DM = NC. AM and BN are two perpendiculars on the side CD. DM = AM. Find the area of the trapezium ABCD.

In the following figure, AD divides BC (BD : CD) in the ratio 2 : 3. A line segment EF and AD is drawn such that CE : EA = 1 : 5 and parallel to each other. If the area of triangle CEF = 1 cm², then what is the area of triangle ABC? (in cm²)

In the following figure, ΔABC is an equilateral triangle of side 12 cm. If AD, BE, and CF are medians of ΔABC, then AD + BE + CF = ?

If the lengths of two sides of a triangle, a and b, are such that the product ab = 24, where a and b are integers, find the number of such possible triangles.

In ∆ABC, D and E are the midpoints of sides BC and AC, respectively. If AD = 10.8 cm, BE = 14.4 cm, and AD and BE intersect at G at a right angle, then the area (in cm²) of ∆ABC is:

In ∆EFG, XY ∥ FG, the area of the quadrilateral XFGY = 44 m². If EX : XF = 2 : 3, then find the area of ∆EXY (in m²).

Find the shaded area?

Find the area of the shaded portion in m²?

△ABC ∼ △ LMN and their perimeters are 72 cm and 48 cm, respectively. If LM = 8 cm, then what is the length of AB (in cm)?

What is the total rooftop area in m² occupied by the triangular bases of all support structures, if 20 panels are installed assuming one support per panel?

The base of parallelogram is 2x² + 5x + 3 and the area is 2x³ + x² – 7x – 6. Find its height.

In the given figure BM = 4 cm and MC = 12 cm, then find AP?

P is any point inside the rectangle ABCD. If PA = 94 cm, PB = 61 cm, and PC = 67 cm, then the length of PD (in cm) is:

In a triangle ABC, D and E are the points on side AC and BC, respectively such that DE∥ AB. F is a point on CE such that DF∥ AE. If FE = 12 cm, and BE = 28 cm, then CF is equal to:-

In a triangle PQR, the length of the side QR is less than twice the length of the side PQ by 3 cm. Length of the side PR exceeds length of the side PQ by 12 cm. If the perimeter of the triangle is 57 cm, then 50% of the length of the smallest side of ΔPQR is equal to:

ABCD is a quadrilateral in which AB || DC, and E and F are the midpoints of the diagonals AC and BD, respectively. If AB = 30 cm, BC = 20 cm, DC = 86 cm, and AD = 84 cm, then what is the length (in cm) of EF?

In ∆TAP, ∠TAP = 60°, TA = 6 cm, AP = 8 cm. K is the midpoint of AP. A line from K is produced to meet TP at O such that ∠AKO = 120°. Find the length of OK.

In ∆ABC, angle B = 90°, AB = 36 cm, BC = 77 cm. If Q is the centroid, then find BQ?

Find the area of the trapezium ABCD?

In △ABC, D and E are the points on sides AB and AC, respectively, such that DE ll BC. If AD = x, DB = x - 2, AE = x + 2, and EC = x - 1, then (AB + EC) is equal to (all measurements in cm):

G is the centroid of the equilateral ΔABC. If AB = 8√3 cm, then the length of AG is equal to:

What is h equal to?

In a right-angled triangle. If the hypotenuse is 101 cm and one of its sides is equal to 20 cm, what is its area (in cm²)?

In the given figure, AD is the angle bisector of ∠CAE, CD = 6 cm, and DE = 8cm. Find the length of BC.

(i) If side QR is 48 cm, what is the length of side RP?

(i) Find the ratio of the sides: QR : RP : PQ.

Let A, B, C be the mid-points of sides PQ, QR PR, respectively, of \(\triangle\)PQR, If the area of \(\triangle\)PQR is 32 cm², then find the area of \(\triangle\)ABC.