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Question

Question 7
Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41cm.

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Solution

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+(40)21681=x2+1600 x2=16811600x2=81 x=81=9 cm
Therefore the breadth of the rectangle is 9 cm.
Perimeter of rectangle = 2(length +breadth)
= 2 (9 +40)
= 2 × 49 = 98 cm
Hence the perimeter of the rectangle is 98 cm.


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