Question

the perimeter of a rectangle is numerically equal to the area of rectangle if the width of rectangle is 15/2 cm then its length is...

Answer 1

Step-by-step explanation:

Let length be L

As the Question says, Perimeter of the rectangle is numerically equal to the Area of rectangle.

Therefore we can conclude,

Perimeter of rectangle = Area of rectangle.

$\sf 2( L + Width ) = L \times Width$

We have been given the width as $\sf \dfrac{15}{2}$ cm.

$\sf \implies 2 \Bigg ( L + \dfrac{15}{2} \Bigg ) = \dfrac{15}{2} \times L$

$\sf \implies 2L + 15 = \dfrac{15}{2} L$

$\sf \implies 2L - \dfrac{15}{2}L = -15$

$\sf \implies L \Bigg ( 2 - \dfrac{15}{2} \Bigg ) = -15$

$\sf \implies L \Bigg ( \dfrac{4-15}{2} \Bigg ) =-15$

$\sf \implies L \Bigg ( \dfrac{-11}{2} \Bigg ) = -15$

$\sf \implies L = \dfrac{2 \times -15}{-11} = \dfrac{30}{11}$

Therefore , the length is $\sf\dfrac{30}{11}cm$

Hope it helps.