ΔABC में  \(\overline {PQ} \ ||\ \overline {AB}\). P और Q क्रमशः BC और CA पर हैं। यदि CQ : QA=1 : 3 और CP=4, तो BC का मान क्या है?

If the ratio of corresponding sides of two similar triangles is √3 ∶ √2 then what is the ratio of the area of the two triangles?

In an equilateral triangle ABC, D is the midpoint of side BC. If the length of BC is 8 cm, then the height of the triangle is:

If the sides of a triangle MNO are 15 cm, 112 cm, and 113 cm then, find the area of the triangle. (in cm²)

In a triangle, ABC, D, and E are two points on the sides AB and AC respectively so DE || BC and AD/BD = 4/5. The ratio of the area of ΔABC to the area of trapezium DECB is?

ΔABC is an isosceles triangle inscribed in a circle. If AB = AC = 12√5 cm and BC = 24 cm then find the radius of the circle.

In the given figure, AB || QP, AB = x , PQ = x + 10. RB= \(\frac{x}{2}\) =, BP= x +1. Find PQ

The area of ΔABC is 104 cm². If D is the midpoint of BC and E is the midpoint of AB, then the area (in cm²) of ΔBDE is :

In the given ΔKMN, PQ is parallel to MN. If KP/PM  = 4/13 and KN 20.4 cm, find KQ

A circle is drawn outside a triangle and the sides of the triangle are 12 cm, 35 cm, and 37 cm then, find the radius of the circle.

If ZXY is a triangle with ZX = ZY = 7 cm and the length of XY is 8 cm. ZO is the Cevian drawn from vertex Z, XZ is 40% more than to the OX then find the length of the OZ.

In △STU, X and Y are the points on sides ST and SU, respectively. XY is parallel to TU. If SX: XT = 2 : 5 and UY = 20 cm, then what is the value of SU?

In ∆ABC, AB = 7cm, BC = 10cm, and AC = 8cm. If AD is the angle bisector of ∠BAC, where D is a point on BC, then DC (in cm) =?

What is the area of a triangle whose sides are of lengths 12 cm, 13 cm and 5 cm?

In ∆PQR, PR = 10 cm. Find the length of PT, where ST∥QR. Given that PS = 6 cm and QS = 14 cm.

In triangle ABC, the bisector of angle BAC cuts the line BC at D. If BD = 6 and BC = 14 then what is the value of AB : AC?

If △ABC is right-angled at ∠B, AB = 12 cm, and ∠CAB = 60°, determine the length of BC.

The base of a triangle is equal to the perimeter of a square whose diagonal is 7√2 cm and its height is equal to the side of a square whose area is 169 cm². The area (in cm²) of the triangle is:

In Δ ABC, D and E are points on sides AB and BC, respectively, such that BD : DA = 1 : 2 and CE :EB = 1 : 4. If DC and AE intersect at F, then FD : FC is equal to:

The side of an equilateral triangle is 24 cm. What will be the radius of in circle of this equilateral triangle?

In a right angled triangled ABC, if ∠ABC = 90º , AB = 6 cm, BC = 8 cm and BD is perpendicular to AC, then AD : DC is:

The sides other than hypotenuse of the right-angle triangular park are in ratio 3 : 4. The sum of all sides is 144 m. Find the area of the triangular park.

In ∆ABC, AD is the internal bisector of ∠A, meeting the side BC at D. If BD = 5 cm, BC = 7.5 cm, then AB : AC is:

The parallel sides of a trapezium and its height are in an arithmetic progression with a common difference of 4. If the height is the highest term and the area of the trapezium is 160 sq. mits, find the ratio of the length of greatest parallel side to that of the smallest parallel side.

In a triangle XYZ, M, and N are the points on sides XY and XZ respectively such that MN || YZ. MN = 3 cm and YZ = 6 cm. Find the ratio of the area of triangle XYZ and parallelogram MNZY.

In the triangle ABC, AB = 12 cm and AC = 10 cm and ∠BAC =60°. What is the value of the length of side BC?

If the ratio of corresponding sides of two similar triangles is √3 ∶ √2 then what is the ratio of the area of the two triangles?

A circle is circumscribed around an equilateral triangle of side 3 cm. What is the area of the circle (in cm²)?

The adjacent sides of a parallelogram are 36 cm and 27 cm in length. If the perpendicular distance between shorter sides is 12 cm, then what is the perpendicular distance between the longer sides ?

Sides of a triangle are 6 cm, 6 cm and 8 cm. What is its area ?

In a right angle triangle ABC, ∠B = 90°. AM and CN are the two medians on side AB and BC such that AM = 10 cm and CN = 5 cm. Find the value of AC.

Three altitudes of length 1.5√3 m, 10√3 m, and 4.5√3 m are drawn on every side of an equilateral triangle from a point that lay inside the triangle. Find the perimeter of the equilateral triangle.

Find the height of the triangle whose base is \(\frac{5}{7}\)th of its height and its area is 18.207 cm².

Sides of a triangle are 9 cm, 6 cm and 5 cm. What is the value of the circumradius of this triangle?

ABCD is a square and points X and Y are on the lines AB and BC respectively such that, XY || AC. If BY : YC = 1 : 3 and area of triangle BXY is 450 cm², find AC.

In the given figure, if AD = 12 cm, AE = 8 cm, and EC = 14 cm, then what is the value (in cm) of 3BD?

In ΔABC , ∠B = 135°, AB = 8√2 cm and BC = 7cm. The length of AC is:

In triangle ABC, M& N is a point on side AB & AC respectively & O is an intersection point of side MC & NB. Given AM : MB =7:9 & MN is parallel to BC. Find the area ratio of ∆MON to ∆BOC?

The sum of the altitude and the base of a triangle is 30 cm. What is the maximum possible area of the triangle?

ΔABC is right-angled at B and D is a point on AC such that BD is perpendicular to AC. If BD = 6 cm and AD = 3 cm, then what will be the length of AC?

In \(\Delta\) PQR, \(\angle\)PQR = 135°, PQ = 8√2 cm and PR = 17 cm. What is the length (in cm) of QR?

In ∆ABC, D is a point on side BC such that ∠ADC = ∠BAC. If CA = 15cm and CD = 9cm, then CB (in cm) =?

In \(\Delta\) ABC, \(\angle\)B 90°. AD and CE are the medians drawn from A and C, respectively. If AC 10 cm and AD √55cm, then the length of CE is:

BD and CE are the medians of ΔABC, right angled at A. If CE = \({5\sqrt{13} \over 2}\) cm, BC = 10 cm, then the length of BD is:

D and E are points on the sides AB and AC, respectively, of △ABC such that DE is parallel to BC and AD: DB is 7:9. If CD and BE intersect each other at F. then find the ratio of areas of △DEF and △CBF.

In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD : DB = 3 : 5. If AC = 5.6 cm, then find the value (in cm) of AE.

If ∆ ABC ~ ∆ FDE such that AB = 9 cm, AC = 11 cm, DF = 16 cm and DE = 12 cm, then the length of BC is:

The area of a triangle is 1470 cm². If the base of this triangle is (3/5)th of the height corresponding to that base, then what will be the height of the triangle?

In a triangle ABC, AB = 6 units, BC = 8 units, and AC = 10 units. Let M be a point on AC such that BM = 5 units. With a point D, a triangle BMD is formed and the triangle BMD is similar to the triangle ABC with \(\frac{BM}{AB}=\frac{BD}{AC}\). What is the length of BD in units?

Find x if ABCD is a parallelogram as given in figure below, with two diagonals AC and BD intersecting at O and OA = x + 3, OB = y + 2, OC = 2x + y, OD = 3y