Question

1. larry has a square porch with sides of length 9 feet. he plans to enlarge it to a rectangular porch by increasing the length by 3 feet and the width by 2 feet. how much bigger in square feet will the new porch be compared to the old porch?

Explanation:

Step1: Calculate the area of the old square porch

The area formula for a square is \(A = s^2\) (where \(s\) is the side - length). Given \(s = 9\) feet, so \(A_{old}=9\times9=81\) square feet.

Step2: Calculate the dimensions and area of the new rectangular porch

The new length \(l=9 + 3=12\) feet and the new width \(w = 9+2 = 11\) feet. The area formula for a rectangle is \(A=l\times w\). Then \(A_{new}=12\times11 = 132\) square feet.

Step3: Calculate the difference in areas

Subtract the area of the old porch from the area of the new porch. \(A_{new}-A_{old}=132 - 81=51\) square feet.

Answer:

51