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The perimeter of the rectangle whose length is 60cm and a diagonal is 61cm Find the perimeter of the rectangle
a) 120cm
b) 142cm
c) 11cm
d) 122cm
Given: The perimeter of the rectangle whose length is 60cm and a diagonal is 61cm.
To find: The perimeter of the rectangle.
Solution:
Formula find perimeter of Rectangle = 2$ (Length + breadth)$
length = 60 cm
breadth = ?
Diagonal = 61 cm
The half of rectangle is right angle triangle.
Diagonal is the hypotenuse. because it will be opposite to right angle 90°
So, apply Pythagoras formula
$Diagonal^2 = length^2 + breadth^2$
$61^2 = 60^2 + breadth^2$
$3721 = 3600 + breadth^2$
$3600 + breadth^2 = 3721$
$breadth^2 = 3721 - 3600$
$ breadth^2 = 121$
breadth $= √121$
breadth $= √11 \times 11$
breadth $ = 11 cm$
So, substitute length and breadth values in perimeter formula
perimeter of Rectangle = $2 [Length + breadth]$
Perimeter of rectangle = $2 [ 60 + 11]$
Perimeter of rectangle = 2 (71)
Therefore , perimeter of Rectangle = 142 cm