In the given figure, if \(\angle\)A=90⁰, \(\angle\)B=90⁰, OB=4.5 cm, OA=6 cm and AP=4 cm, then find the QB.

If ratio of corresponding sides of two similar triangles is 5 : 6, then find ratio of their areas.

In given figure DE || BC. If AD=3 cm, DB=4 cm and AD=6 cm, then find EC.

In the figure, PQ is parallel to MN. If \(\frac { K }{ PM } =\frac { 4 }{ 13 } \) and KN=20.4 cm, then find KQ.

If triangle ABC is similar to triangle DEF such that 2AB = DE and BC = 8 cm, then find EF.

In a right angled triangle, if hypotenuse is 20 cm and the ratio of other two sides is 4 : 3, find the other sides.

An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side.

ABCD is a trapezium in which \(AB\parallel DC\). P and Q are points on sides AD and BC respectively such that \(PQ\parallel AB\). If PD = 18 cm, BQ = 35 cm and QC = 15 cm, find the value of AD.

A girl of height 100 cm is walking away from the base of a lamppost at a speed of 1.9 m/s. If the lamp is 5 m above the ground, find the length of her shadow after 4s.
 

In \(\triangle\)ABC, \(AD\bot BC,\)such that AD²=BD x CD. Prove that \(\triangle\)ABC is right angles at A.

It is given that \(\triangle ABC\sim \triangle EDF\) such that AB = 5 cm, AC = 7 cm, DF = 15 cm and DE = 12 cm. Find the lengths of the remaining sides of the triangles.

If D and E are points on the respective sides AB and AC of \(\triangle ABC\) such that AD = 6 cm. BD = 9 cm, AE = 8 cm, EC = 12 cm. Prove that \(DE\parallel BC\).

State which of the two triangles given in the figure are similar? Also, state the similarity criterion used.

In the given figure, if  \(DE\parallel BC\), find the ratio of ar \(\left( \triangle ADE \right) \) and ar \(\left( \triangle DECB \right) \)

Prove that the area of the equilateral triangle described on the side of an isosceles right angled triangle is half the area of the equilateral triangle described on its hypotenuse.

If the areas of two similar triangles are respectively 81 cm² and 49 cm²  Find the ratio of their corresponding medians.

If the sides of a triangle are 3 cm, 4 cm and 6 cm long, then determine whether the triangle is a right angled triangle.

Let \(\triangle ABC\sim \triangle DEF\) and their areas be respectively 64 cm² and 121 cm² If EF = 15.4 cm² then find BC.

Sides of triangles are given below. Determine which of them are right angled triangles? In case of a right angled triangle, write the length of its hypotenuse.
7 cm, 24 cm and 25 cm

In the given figure, if \(\triangle ADB\sim \triangle ADC\), then find the value of p.