Question

A square painting is surrounded by a frame. The outside edges of the frame or X inches in length and there is a 5 inch border between painting in the frame. What is the total area of the border

Answer 1

Answer:

Step-by-step explanation:

The area of a square of side, $s$, is given by $s^2$

The area of the frame with the painting is $x^2$.

Because there is a 5 inch border between the painting and the frame, the side length of the painting is $x-5$. Hence the area of the painting is $(x-5)^2$.

The total area of the border is the difference of the two areas:

$A = x^2 - (x-5)^2$

$A = x^2 - (x^2 - 10x + 25)$

$A = x^2 - x^2 + 10x - 25$

$A = 10x - 25$