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

Answer:

Step-by-step explanation: Let the shorter side[breadth] and larger side[Length] be "x" and "y" respectively.

According to given condition"

Breadth = x

Diagonal = x+60 and

Length  = x + 30

Diagonal will create the right angle triangle so we'll use Pythagoras theorem to solve this problem.

Diagonal^2 = Length^2 + Breadth^2;

(x + 60)^2 = (x + 30)^2 + x^2

After solving above equation we'll get  x = 90

So Breadth = 90 Meters, Length = 120 Meters and Diagonal =  150 Meters

Answer 2

Answer:

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.