Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.

Given diagonal (PR) = 41 cm, length (PQ) = 40 cm
Let breadth (QR) be x cm.
Now, in right angled triangle PQR,

(PR)² = (RQ)² + (PQ)² [By Pythagoras theorem]
⇒ (41)² = x² + 1600
⇒ 1681 = x² + 1600
⇒ x² = 1681 – 1600
⇒ x² = 81
⇒ x= √81 = 9 cm
Therefore the breadth of the rectangle is 9 cm.
Perimeter of rectangle = 2(length + breadth)
= 2 (9 + 49)
= 2 x 49 = 98 cm
Hence, the perimeter of the rectangle is 98 cm.

Class 7 Maths Chapter 6 Exercise 6.5

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