Question

the length of a rectangle is 5cm greater than the width. the area of the rectangle is 84cm squared. find the length and width

Answer 1

Answer:

Therefore,

$Length=12\ cm$

$Width= 7\ cm$

Step-by-step explanation:

Let the Width of rectangle be 'x' cm.

Then the length of a rectangle will be (x + 5) cm.

Area of rectangle given is 84 cm squared.

To Find:

Length = (x+5) = ?

Width = x = ?

Solution:

We have area of rectangle given as

$\textrm{Area of Rectangle}=Length\times Width$

Substituting the given values we get

$84=(x+5)x\\x^{2} +5x-84=0$

On factorizing we get

$x^{2} +12x-7x-84=0\\x(x+12)-7(x+12)=0\\(x+12)(x-7)=0\\(x+12)=0\ or\ (x-7)=0\\x=-12\ or\ x=7\\\therefore x =7\ cm\ \textrm{As x cannot be negative}$

Therefore,

$Length=x+5=7+5=12\ cm$

Therefore,

$Length=12\ cm$

$Width= 7\ cm$