Question

the length of a rectangle is one unit more than its width. if the area of the rectangle is 56 square units,find the dimensions of the rectangle​

Answer 1

7

Step-by-step explanation: POV: I got it right

Answer 2

Given:

The length of a rectangle is one unit more than its width.

Area of rectangle = 56 units

To find:

The dimensions of the rectangle​.

Solution:

Let, width of the rectangle be x.

Then, length of the rectangle = x+1

Area of a rectangle is

`Area=length* width`

`56=(x+1)* x`

`56=x^2+x`

`0=x^2+x-56`

By splitting the middle term, we get

`x^2+8x-7x-56=0`

`x(x+8)-7(x+8)=0`

`(x-7)(x+8)=0`

Using zero product property, we get

`x-7=0` and
`x+8=0`

`x=7` and
`x=-8`

Width cannot be negative. So, x=7.

Now,

Width = 7 units

Length = 7+1

= 8 units

Therefore, the length of the rectangle is 8 units and width is 7 units.