Question

find the diagonal of rectangle whose area is 660 m and perimeter is 142 m
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Answer 1

Answer:

Diagonal of the Rectangle is 61 meters.

Step-by-step explanation:

Given,

Area of the rectangle is 660 m² .

perimeter of the rectangle is 142 meters.

let, the length of the rectangle is 'α' meters.

     the breadth of the rectangle is 'β' meters.

Then, the area of the rectangle is A = (α×β ) m²

And , the perimeter of the rectangle is S =2×(α+β) meters

∴ (α×β) = 660 m²

  2×(α+β) = 142 meters  ⇒ (α+β) = 71 meters

Hence, the length of the diagonal of the rectangle is,

D = √( α² + β² )

    = √{ ( α+β)² - 2×(α×β) }

    = √{ 71² - (2×660) }

    =√{ 5041 - 1320}

    =√3721

    = 61 meters