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

Therefore,

`Length=12\ cm`

`Width= 7\ cm`

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* 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`