A day full of math games & activities. Find one near you.

A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a
(a) square
(b) rectangle
(c) rhombus
(d) trapezium

Solution:

Given, PQRS is a parallelogram.

The sides QR = 6 cm, PQ = 4 cm.

The measure of ∠PQR = 90°.

We have to find the type of quadrilateral.

A parallelogram is a quadrilateral with two pairs of parallel sides.

The length and breadth of the parallelogram are 6 cm and 4 cm.

The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.

One angle is equal to 90 degrees. So, the opposite angle is also 90 degrees.

We know that the Sum of all the interior angles equals 360 degrees.

All the angles of the given parallelogram are equal to 90 degrees.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all four vertices are equal to 90 degrees.

Therefore, PQRS is a rectangle.

✦ Try This: A parallelogram ABCD is constructed with sides AB = 5 cm, BC = 1.5 cm and ∠A = C. Then ABCD is a (a) square, (b) rectangle, (c) rhombus, (d) trapezium

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 46

A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a (a) square (b) rectangle (c) rhombus (d) trapezium

Summary:

A parallelogram PQRS is constructed with sides QR = 6 cm, PQ = 4 cm and ∠PQR = 90°. Then PQRS is a rectangle.

☛ Related Questions: