Question

The diagonal of a rectangle is 28m more than is breadth and the length is 14m more than its breadth. Find the length and breadth of the rectangle.​

Answer 1

Step-by-step explanation:

Given:-

• The diagonal of the rectangle is 28cm more than its breadth.

• Length is 14m more than its breadth.

To Find:-

• The length and breadth of the rectangle.

Solution:-

Let the breadth of the rectangle be x

Length of the rectangle = 14 + x

Diagonal of the rectangle = 28 + x

In a rectangle:-

(Diagonal)² = (Length)² + (Breadth)²

$\sf \implies {(28 + x)}^{2} = {x}^{2} + {(14 + x)}^{2}$

$\sf \implies {28}^{2} + {x}^{2} + 2(28)(x)= {x}^{2} + {14}^{2} + {x}^{2} + 2(14)(x)$

$\sf \implies 784+ {x}^{2} + 56x= 2{x}^{2} + 196 +28x$

$\sf \implies 2 {x}^{2} - {x}^{2} - 56x + 28x= 784 - 196$

$\sf \implies {x}^{2} - 28x= 588$

$\sf \implies {x}^{2} - 28x - 588 = 0$

By splitting the middle term:-

$\sf \implies {x}^{2} - 42x + 14x - 588 = 0$

$\sf \implies {x}(x - 42) + 14(x - 42)= 0$

$\sf \implies (x - 42)(x + 14)= 0$

$\sf \implies x - 42 = 0 \: \: \: (or) \: \: \: x + 14= 0$

$\sf \implies x = 42 , -14$

Since, Breadth of a rectangle cannot be negative.

Breadth of the rectangle = 42m

Length of the rectangle = 14 + x = 14 + 42 = 56cm

Therefore:-

The length and breadth of the rectangle are 42cm and 56cm respectively.