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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
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Solution
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
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