Question

If a rectangle is 4 inches wide and 7 inches long. When the length and width are increased by the same amount, the area is increased by 26 square inches. What are the new dimensions.

Answer 1

New length =
`2+7=9` inches

New width =
`2+4=6` inches

Explanation:

Given:

Length of rectangle is 7 inches

Width of a rectangle is 4 inches

The area is increased by 26 square inches when the length and width are increased by the same amount.

To find: new length and width

Solution:

With length of rectangle is 7 inches and width of a rectangle is 4 inches,

area = 7×4 = 28 inches

Let length and width be increased by x inches

New length = x + 7 inches

New Width = x + 4 inches

New area =
`(x+7)(x+4)=x^2 +11x+28`

Also, new area = 28 + 26 = 54 square inches.

So,

`28+11x+x^2 =54\\x^2+11x-26=0\\x^2 +13x-2x-26=0\\x(x+13)-2(x+13)=0\\(x-2)(x+13)=0\\x= 2, -13`

As dimension can not be negative,
`x=-13` is rejected.

So,
`x=2`

New length =
`2+7=9` inches

New width =
`2+4=6` inches