Question

The diagonal of a rectangular field is 60m more than the shorter side if the longer side is 30 m more than the shorter side find the sides of the field

Answer 1

Answer:

Let the shorter side of the rectangle be x m.

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

⇒ x2 + (x + 30)2 = (x + 60)2

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

⇒ x2 - 60x - 2700 = 0

⇒ x2 - 90x + 30x - 2700 = 0

⇒ x(x - 90) + 30(x -90)

⇒ (x - 90)(x + 30) = 0

⇒ x = 90, -30

However, side cannot be negative. Therefore, the length of the shorter side will be 90 m.

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

Answer 2

Solution:-

Let the shorter side of rectangle be (x) m.

Then ,the diagonal of rectangle will be (x+60)m

And the longest side of rectangle will be (x+30)m

Let the length be longest sude and breadth be shortest side of rectangle.

As we know that,

(diagonal)² = (length)² + (breadth)²

(x+60)² = (x+30)² + (x)²

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

x² - 60x - 2700 = 0

x² - 90x + 30x -2700 = 0

x(x-90) + 30(x-90) = 0

(x - 90)(x + 30) = 0

x = 90 or x = -30

Hence , x = 90 because side never be negative.

So that,

Breadth = 90m

Length = (x + 30) = (90 + 30) = 120m

Hence the length will be 120m and breadth will be 90m.

Hope its help uh❤