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 centroid of an equilateral triangle PQR is L. If PQ = 6 cm, the length of PL is:

The difference between the length of two parallel sides of a trapezium is 12 cm. The perpendicular distance between these two parallel sides is 60 cm. If the area of the trapezium is 1380 cm², then find the length of each of the parallel sides (in cm).

In ∆ABC the straight line parallel to the side BC meets AB and AC at the points P and Q, respectively. If AP = QC, the length of AB is 12 cm and the length of AQ is 2 cm, then the length (in cm) of CQ is:

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

L and M are the mid points of sides AB and AC of a triangle ABC, respectively, and BC = 18 cm. If LM || BC, then find the length of LM (in cm).

In ∆ABC, P is a point on AB such that PB : AP = 3 : 4 and PQ is parallel to AC. If AR and QS are perpendicular to PC and QS = 9 cm, what is the length (in cm) of AR?

If the areas of two similar triangles are in the ratio 196 : 625, what would be the ratio of the corresponding sides?

In a trapezium ABCD, AB, and DC are parallel to each other with a perpendicular distance of 8 m between them. Also, (AD) = (BC)= 10 m, and (AB) = 15 m < (DC). What is the perimeter (in m) of the trapezium ABCD?

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

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

The perimeter of a triangle with sides of integer values is equal to 13. How many such triangles are possible?

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

∆ABC ~ ∆DEF such that AB = 9.1 cm and DE = 6.5 cm. If the perimeter of ∆DEF = 25 cm, then the perimeter of ∆ABC is:

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?

In a ∆ABC, two medians AD and BE intersect at G at right angles. If AD = 18 cm and BE = 12 cm, then the length of BD is equal to:

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:

Which of the following are the sides of a right-angled triangle?

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?

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?

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

Given that the perimeters of two similar triangles, ∆ABC and ∆DEF, are 24 cm and 9 cm, respectively, and DE = 3 cm, what is the ratio between the area of ∆ABC and that of ∆DEF?

In a ΔABC, the median BE intersects AC at E. If BG = 12 cm, where G is the centroid, then BE is equal to:

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

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?

The lengths (in cm) of three sides of a triangle are, respectively, 48, 55 and 73. What is the length (in cm) of the median joining the mid-point of the longest side to its opposite vertex?

The triangle has sides 3 cm, 4 cm, and 5 cm. What is the length of the perpendicular from the opposite vertex to the side whose length is 5 cm?

If \(\Delta ABC\approx\Delta QRP,\frac{Ar(\Delta ABC)}{Ar(\Delta QRP)}\)\(=\frac{9}{4}\), AB = 18 cm, BC = 15 cm, then the length of PR is:

ΔXYZ ~ ΔGST and XY : GS = 2 : 3, XV is the median to the side YZ, and GD is the median to the side ST. The value of \(({{YV} \over SD})^2\)  is__________.

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

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

If the hypotenuse of a right-angled triangle is 29 cm and the sum of the other two sides is 41 cm, then the difference between the other two sides is:

The area ofa trapezium shaped field is 1785 square feet. The distance between the two parallel sides is 35 feet and one of the parallel sides is 42 feet long. What is the length of the other parallel side?

The sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 90 cm. Find its area (in cm² ).

The midpoints of AB and AC of a ∆ABC are X and Y, respectively. If BC + XY = 24 units, then the value of BC - XY is:

In an equilateral ∆PQR, S is a point on the side QR such that QR = 3QS. If PQ = 9 cm, then what will be the length (in cm) of PS?

The area of a trapezium is 100 cm². If the distance between the parallel sides of the trapezium is 10 cm, then what is the sum of the lengths of the two parallel sides?

In ∆ABC with sides 8 cm, 9 cm, and 12 cm, the angle bisector of the largest angle divides the opposite sides into two segments. What is the length of the shorter segment?

The lengths of the parallel sides of a trapezium are 10 cm and 20 cm. If the distance between these parallel lines is 5 cm, then what is the area of the trapezium?

The length of two parallel sides of a trapezium are 15 metre and 20 metre. If its height is 22 metre, then what is the area of the trapezium?

AD is the median of triangle ABC. P is the centroid of triangle ABC. If AP = 14 cm, then what is the length of PD?

For a triangle, ABC, D, and E are two points on AB and AC such that AD = \({{1} \over 6}\)AB,  AE = \({{1} \over 6}\)AC. If BC = 22 cm, then DE is __________.(Consider up to two decimals)

In triangle ABC, the bisector of angle BAC cuts the side BC at D. If AB = 10 cm, and AC = 14 cm, then what is BD : DC ?

The areas of the two triangles are in the ratio 4 : 3 and their heights are in the ratio 6 : 5. Find the ratio of their bases.

In an equilateral triangle ABC, D, E and F are the mid points of AB, BC and AC respectively.The quadrilateral BEFD is a: 

Suppose ΔABC be a right-angled triangle where ∠A = 90° and AD ⊥ BC. If area (ΔABC) = 80 cm² and BC = 16 cm, then the length of AD is:

The perimeter of an equilateral triangle is equal to the circumference of a circle. If each side of this equilateral triangle is 88 cm long, then what will be the length of the diameter of the circle? 

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

Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.

In a triangle, LMN, OP is a line segment drawn parallel to the side MN. OP intersects the sides LM and LN at O and P, respectively. If LM = 15 cm, OM = 4 cm, and PN = 5 cm, then what is the length (in cm) of the side LN?