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

In quadrilateral ABCD, side AB is the longest and side DC is the shortest.
Prove that: D > B.

In the following figure; AB is the largest side and BC is the smallest side of triangle ABC.
Write the angles x^o, y^o and z^o in ascending order of their values.

In the following diagram; AD = AB and AE bisect angle A.

Prove that:
(i) BE = DE
(ii) ∠ABD > ∠C

P is any point inside the triangle ABC.
Prove that: ∠BPC > ∠BAC.

In the following figure, ABC is an equilateral triangle and P is any point in AC;
prove that: BP > PC

In a quadrilateral ABCD; prove that:
(i) AB+ BC + CD > DA
(ii) AB + BC + CD + DA > 2AC
(iii) AB + BC + CD + DA > 2BD

Using ruler and compasses only, construct a rectangle each of whose diagonals measure 6 cm and the diagonals interest at an angle of 45^o.

Construct a rectangle ABCD, when:
Its sides are 6.0 cm and 7.2 cm.

Construct a rectangle ABCD, when:
One side = 4 cm and one diagonal is 5 cm. Measure the length of the other side.

Construct a rectangle ABCD, when:
One diagonal = 6.0 cm and the acute angle between the diagonals = 45^o.

Construct a rectangle ABCD, when:
Area = 24 cm² and base = 4.8 cm².

Construct a rectangle ABCD, when:
Area = 36 cm² and height = 4.5 cm.

The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.

The distance between parallel sides of a trapezium is 15 cm and the length of the line segment joining the mid-points of its non-parallel sides is 26 cm. Find the area of the trapezium.

The area of a parallelogram is y cm² and its height is h cm. The base of another parallelogram is x cm more than the base of the first parallelogram and its area is twice the area of the first. Find, in terms of y, h, and x, the expression for the height of the second parallelogram.

Find the area of a quadrilateral one of whose diagonals is 30 cm long and the perpendiculars from the other two vertices are 19 cm and 11 cm respectively. 

A wire when bent in the form of a square encloses an area = 576 cm². Find the largest area enclosed by the same wire when bent to form;
(i) an equilateral triangle.
(ii) A rectangle whose adjacent sides differ by 4 cm.

A rectangular plot of land measures 45 m x 30 m. A boundary wall of height 2.4 m is built all around the plot at a distance of 1 m from the plot. Find the area of the inner surface of the boundary wall.

The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles; find the area of the quadrilateral.

ABCD is a square with each side 12 cm. P is a point on BC such that area of  ΔABP: area of trapezium APCD = 1: 5. Find the length of CP.