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.

For maths expert ​

Answer 1

☛ Let the shorter side be x.

Therefore, the diagonal = x + 60 & the longer side = x + 30.

Since length can't be negative, therefore, the shorter side is 90m & the longer side is 120m.

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Answer 2

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 out:

Find the sides of the field?

Solution:

Let shorter side of rectangle be x m .

Then longer side = ( x + 30 ) m and Diagonal = ( x + 60 ) m

Using pythagoras therome, we have

AC² = AB² + BC²

⇒ ( x + 60 )² = ( x + 30 )² + x²

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

⇒ x² - 60x - 2700 = 0

⇒ x² - 90x + 30x - 2700 = 0

⇒ x ( x - 90 ) + 30 ( x - 90 ) = 0

⇒ ( x - 90 ) ( x + 30 ) = 0

⇒ x - 90 = 0 or x + 30 = 0

⇒ x = 90 or - 30

Therefore, Shorter side = x = 90 cm

And, Longer side = ( x + 30 ) cm = ( 90 + 30 ) cm = 120 cm