(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

If s = `"n"/(2)[2"a" + ("n" - 1)"d"]`, the n express d in terms of s, a and n. find d if n = 3, a = n + 1 and s = 18.

"Area A oof a circular ring formed by 2 concentric circles is equal to the product of pie and the difference of the square of the bigger radius R and the square of the bigger radius R and the square of the smaller radius r. Express the above statement as a formula. Make r the subject of the formula and find r, when A = 88 sq cm and R = 8cm.

Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.

Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.

A man goes 10 m due east and then 24 m due north. Find the distance from the straight point.

A ladder 25m long reaches a window of a building 20m above the ground. Determine the distance of the foot of the ladder from the building.

A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.

A ladder 15m long reaches a window which is 9m above the ground on one side of a street. Keeping its foot at the same point, the ladder is turned to other side of the street to reach a window 12m high. Find the width of the street.

The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?

Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.

The length of the diagonals of rhombus are 24cm and 10cm. Find each side of the rhombus.

Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.

In ΔABC, AD is perpendicular to BC. Prove that: AB² + CD² = AC² + BD²

In an equilateral triangle ABC, the side BC is trisected at D. Prove that 9 AD² = 7 AB².

From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF² + BD² + CE² = OA² + OB² + OC² - OD² - OE² - OF²

From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF² + BD² + CE² = AE² + CD² + BF²

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC² = AD² + BC x DE + `(1)/(4)"BC"^2`

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB² = AD² - BC x CE + `(1)/(4)"BC"^2`

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB² + AC² = 2AD² + `(1)/(2)"BC"^2`

In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC² - AB² = 2BC x ED