Question 107

A rectangular plot of perimeter 46 meters has area of 120 sq. meters. The length (in meters) of its diagonal is

Solution

Let length = l

Breadth = b

Given, lb=120 and l+b = 23

Squarring on both sides, $$l^2+b^2+2lb\ =\ 529$$

$$l^2+b^2=\ 529\ -\ 2\left(120\right)$$

=> $$l^2+b^2=\ 289$$

Lenth of diagonal = $$\sqrt{l^2+b^2\ }=\ \sqrt{\ 289}\ =17$$

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