Question

If the perimeter of a rectangle is 42 m and it's diagonal is 15m .find the length of sides?

Answer 1

Given:

Perimeter = 42 m

Diagonal = 15 m

To Find:

Length of the sides

Formulae Needed:

$\text{Perimeter of a rectangle } = 2 (\text{Length} + \text{Breadth} )$

$\text{ Pythagoras Theorem : } a^2 + b^2 = c^2$

Solution

Define x:

Let the length of the rectangle be x.

Find the breadth of the rectangle in term of x:

$\text{Perimeter of a rectangle } = 2 (\text{Length} + \text{Breadth} )$

$42= 2 (x + \text{B} )$

$42= 2 x + 2 \text{B}$

$2\text{B} = 42 - 2x$

$\text{B} = 21 - x$

Solve x:

The 2 sides of the rectangle and the diagonal will form a right angle triangle.

$a^2 + b^2 = c^2$

$x^2 + (21 - x)^2 = 15^2$

$x^2 + 21^2 + x^2 - 42x = 15^2$

$2x^2 - 42x + 21^2 - 15^2= 0$

$2x^2 - 42x + 216= 0$

$2 (x - 9) (x - 12) = 0$

$x = 9 \text { or } x = 12$

Find the length and the breadth:

$\text{Length } = x$

$\text{Length } = 12 \text { m}$

$\text{Breadth } = 21 - x$

$\text{Breadth } = 21 - 12$

$\text{Breadth } = 9 \text { m}$

Answer; the length is 12 m and the breadth is 9 m