Question

a photograph is printed in the center of a piece of paper measuring 7 cm by (x + 8) cm. The photo measures 5 cm by (x +6) cm . The area of the border around the photograph is 50 cm ( squared )

Answer 1

The paper is 7 cm by (x + 8) cm.

A photo is 5 cm by (x + 6) cm, and is printed in the middle of the paper.

The area of the border/space around the photo is 50 cm².

To find the area of the border around the photo, you find the area of the paper and subtract it by the area of the photo.

The area of the paper:

A = 7 · (x + 8)

The area of the photo:

A = 5 · (x + 6)

Your equation to find the area of the border around the photo is:

(7 · (x + 8)) - (5 · (x + 6)) = A

[area of paper - area of photo = area of border]

Since you know the area of the border, you can plug it in:

(7 · (x + 8)) - (5 · (x + 6)) = 50

Multiply the 7 into (x + 8), and multiply the 5 into (x + 6)

(7x + 56) - (5x + 30) = 50

Distribute/multiply the - to (5x + 30)

7x + 56 - 5x - 30 = 50

Combine like terms

2x + 26 = 50

Subtract 26 on both sides

2x = 24

Divide 2 on both sides

x = 12