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

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Updated on: 10-Oct-2022

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