Question

1. calculate the area of the figure. then, determine what happens to the area of the rectangle when you double the length of each side 15 in. 1 in.

Explanation:

Step1: Calculate original area

The area formula for a rectangle is $A = l\times w$. Given $l = 15$ in and $w = 7$ in, so $A_1=15\times7 = 105$ in².

Step2: Double the side - lengths

The new length $l_2 = 2\times15=30$ in and the new width $w_2 = 2\times7 = 14$ in.

Step3: Calculate new area

Using the area formula again, $A_2=l_2\times w_2=30\times14 = 420$ in².

Step4: Analyze the change in area

To find out how the area changes, we divide the new area by the original area: $\frac{A_2}{A_1}=\frac{420}{105}=4$. So the area is multiplied by 4 when the length of each side is doubled.

Answer:

The original area of the rectangle is 105 in². When the length of each side is doubled, the new area is 420 in², and the area of the rectangle is multiplied by 4.