#### Question: The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

#### Video Explanation

#### Explanatory Answer

Let the shorter side BC measure x units.

The diagonal is 60 metres more than the shorter side.

So, diagonal AC = x + 60

Length is 30 metres more than the shorter side.

So, length AB = x + 30

In right triangle, ABC, AC^{2} = AB^{2} + BC^{2}

So, (x + 60)^{2} = (x + 30)^{2} + x^{2}

x^{2} + 120x + 3600 = x^{2} + 60x + 900 + x^{2}

x^{2} – 60x – 2700 = 0

##### Factorize the equation to find x

x^{2} – 90x + 30x – 2700 = 0

x(x – 90) + 30(x – 90) = 0

(x – 90)(x + 30) = 0

x = 90 and x = -30.

'x' is the measure of the shorter side of the rectangle.

The measure of the shorter side cannot be negative.

Therefore, shorter side measures 90 m.

Measure of longer side = x + 30 = 90 + 30 = 120 m