Question

The diagonals of a rectangular field is 60 m more than the shorter side if the largest side is 30 m more than the shorter side find the sides of the field​

Answer 1

$\huge\bold\green{answer}$

We have,

Long side of rectangular field is 60 meters more then the shorter side.

Let the longer side will be (y+30)mtr.

And the length of the diagonal will be (y+60) mtr.

Now, According to given question.

Using Pythagoras theorem,

(Diagonal)² = (shorterside)² + (longerside)²

(y+60)² = y² + (y+30)²

⇒y² + 3600 + 120y = y² + y² + 900 + 60y

⇒3600 + 120y − y² − 900 − 60y = 0

⇒ −y² + 60y + 2700 = 0

⇒ y² − 60y − 2700 = 0

⇒y² − (90−30)y − 2700 = 0

⇒y² − 90y + 30y − 2700 = 0

⇒ y(y−90) + 30 (y−90) = 0

⇒(y−90) (y+30) = 0

If,

y + 30 = 0

y = − 30 (not possible)

If,

y − 90 = 0

y = 90

So, the length of shorter side = y − 30 = 90 − 39 = 60

Longer side 90 + 30 = 120

Hence, this is the answer.