Question

a picture is 5 inches by 7 inches. there is a frame around the picture that is of uniform width. the area of the frame and the picture combined is 72 in². how wide is the picture frame? formulate an equation that you would use to solve for x, the width of the picture frame. a ((5 + x)(7 + x) = 72) b ((5 - x)(7 - x) = 72) c ((5 + 2x)(7 + 2x) = 72) d ((5 - 2x)(7 - 2x) = 72)

Explanation:

Step1: Analyze the dimensions with the frame

The picture has dimensions 5 inches (width) and 7 inches (height). The frame has a uniform width \( x \). So, on both sides of the picture (left and right), the width added is \( 2x \) (since the frame is on both sides). Similarly, for the height, the frame adds \( 2x \) (top and bottom). So the total width of the picture + frame is \( 5 + 2x \) and the total height is \( 7 + 2x \).

Step2: Recall the area formula for a rectangle

The area of a rectangle is \( \text{length} \times \text{width} \). Here, the combined area of the picture and the frame is 72 \( \text{in}^2 \). So the equation should be \( (5 + 2x)(7 + 2x)=72 \), which corresponds to option C.

Answer:

C. \((5 + 2x)(7 + 2x)=72\)