Question

The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.

Options

• 120 cm

• 122 cm

• 71 cm

• 142 cm

Answer 1

The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is 142 cm.

Explanation:

Consider the rectangle PQRS,

Given, length of rectangle PQ = 60 cm, Diagonal of the rectangle = 61 cm.

To find out the height of the rectangle, consider the right angled triangle PQR.

From the Pythagoras theorem,

PR² = PQ² + RQ²

⇒ 61² = 60² + RQ²

⇒ 3721 = 3600 + RQ²

⇒ RQ² = 3721 – 3600

⇒ RQ² = 121

⇒ RQ = `sqrt(121)`

⇒ RQ = 11 cm

Then, the perimeter of the rectangle PQRS = 2(Length + Breadth)

= 2(60 + 11)

= 2(71)

= 142 cm