Question

One side of a rectangle is 10 cm longer than its width.The area of rectangle is 96 sq.cm. Find the dimensions of the rectangle?

Answer 1

`color (red)(=6cm & 16cm`

Explanation:

Let one side of the rectangle be `x`, Other side=`x+10`

Area of rectangle= `lxxb`

`96= x xx(x+10)`

`96=x^2+10x`

`x^2+10x-96=0`

Identity:
`color(magenta)(x^2+(a+b)x+ab=(x+a)(x+b)`

`x^2+16x-6x-96=0`

`x(x-6)+16(x-6)=0`

`(x-6)(x+16)=0`

`therefore x-6=0 orx+16=0`

`If x-6+0,` then `x=6`

`If x+16=0,` then `x=-16`

Since `x` cannot take a `-ve` value, x=6

`therefore,` the sides are `=x & x+10`

`color (red)(=6cm & 16cm`

~Hope this helps! :)