Question

A rectangular photograph is mounted on a square piece of cardboard whose sides have length x. The border that surrounds the photo is 3 inches on each side and 4 inches on both the top and the bottom. Which of the following expressions represents the area of the photograph? Select all that apply. A:xsquared B:(x+8)(x+6) C:(x-8)(x-6) D:xsquared +48 E:xsquared -48 F:xsquared+14x+48 G:xsquared-14x+48

Answer 1

Answer:

option (C) and (G) is correct.

The area of photograph is (x - 8)(x -6) inches² or $x^2-14x+48$ inches².

Step-by-step explanation:

Given : A rectangular photograph is mounted on a square piece of cardboard whose sides have length x. The border that surrounds the photo is 3 inches on each side and 4 inches on both the top and the bottom.

We have to find the expressions that represents the area of the photograph.

We first draw the figure according to given dimensions.

Area of rectangle  is length × breadth

Length of rectangle (x - 4 - 4) = (x - 8) inches

Breadth of rectangle (x -3 - 3) = (x -6) inches

Thus, area of photograph  = (x - 8)(x -6) inches².

Simplify, we get,

area of photograph  =$(x - 8)(x -6)=x^2-14x+48$ inches².

Thus, the area of photograph is (x - 8)(x -6) inches² or $x^2-14x+48$ inches².

Thus, option (C) and (G) is correct.

Answer 2

Answer:

Area of the photograph is $(x-8)(x-6)$

Step-by-step explanation:

The piece of cardboard is a square with side length as x.

The border that surrounds the photo is 3 inches on each side. So the length of the photograph is reduced by 3 inches for 2 times.

Hence, the length of photograph is =$x-(2\times 3)=x-6$

The border also surrounds the photo is 4 inches on both the top and the bottom. So the width of the photograph is reduced by 4 inches for 2 times.

Hence, the width of photograph is =$x-(2\times 4)=x-8$

The area of the photograph will be,

$=\text{Length}\times \text{Width}\\\\=(x-8)(x-6)$