Question

A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

Answer 1

width of the border is 3 inches

Explanation:

Given data

size = 8 inches by 10 inches

area = 144 square inches

to find out

width of the border

solution

first we consider width of border is x

area of new full rectangle = (8 + 2x ) × ( 10 + 2x )

so we know area of photo = 8 × 10 = 80 square inches

and area of border = 144 square inches that is given

so new area of photo with the border is 80 + 144 = 224 square inches

and we can say that

area of full rectangle - area of the photograph = Area of Border

(8 + 2x) × (10 + 2x) – (80) = 144 square inches

80 + 16x + 20x +
`4x^(2)` – 80 = 144

`4x^(2)` + 36x – 144 = 0

solve thios equation we get

`2x^(2)` + 9x – 36 = 0

solve thios equation we get

(x + 12) (x – 3) = 0

so here x have two value one is negative and other is positive

so we consider only positive value

x = -12 or x = 3

width of the border is 3 inches