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.​

Answer 1

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Let us say, the shorter side of the rectangle be x m.

Then, larger side of the rectangle = (x + 30) m

As given, the length of the diagonal is = x + 30 m

Therefore,

⇒ x^2 + (x + 30)^2 = (x + 60)^2

⇒ x^2 + x^2 + 900 + 60x = x^2 + 3600 + 120x

⇒ x^2 – 60x – 2700 = 0

⇒ x^2 – 90x + 30x – 2700 = 0

⇒ x(x – 90) + 30(x -90) = 0

⇒ (x – 90)(x + 30) = 0

⇒ x = 90, -30

However,

side of the field cannot be negative.

Therefore,

the length of the shorter side will be 90 m.

and the length of the larger side will be (90 + 30) m = 120 m.

Answer 2

$\bf\:{\underline{Given}}:-$

• The diagonal of a rectangular field is 60 metres more than the shorter side.

• The longer side is 30 metres more than the shorter side.

To find :-

• The sides of the field

Solution :-

Let shorter side be x m

diagonal = ( x + 60) m

longer side = (x + 30) m

In right ∆ ABC

(AC)² = (AB)² + (BC)²

➝ (x + 60)² = (x)² + (x + 30)²

➝ (x)² + 2 × x × 60 + (60)² = x² + (x)² + 2 × x × 30 + (30)²

➝ x² + 120x + 3600 = x² + x² + 60x + 900

➝ x² + 60x + 900 - 120x - 3600 = 0

➝ x² - 60x - 2700 = 0

➝ x² - 90x - 30x - 2700 = 0

➝ x(x - 9) + 30(x - 90) = 0

➝ (x - 90) ( x + 30) = 0

Now,

➝ (x - 90) = 0

➝ x = 0 + 90

➝ x = 90

Then,

➝ (x + 30) = 0

➝ x = 0 - 30

➝ x = -30

Hence,the side of the field cannot be negative so, the length of the shorter side will be 90m.

and length of longer side will be (x + 30) = (90 + 30) = 120 m.