Question

1. megan’s room was remodeled. the new area of the room is 175% of the previous area. only the length of the room changed.

image of a square with side 4 m and an extension of length x

by how many square meters has the area of megan’s room increased? explain.
the area of megan’s room increased by 4, 12, 16, 28 m².
the original area was 4, 12, 16, 28 m²,
75% of 4, 12, 16, 28 is 4, 12, 16, 28.

Explanation:

Step1: Find original area

The original room is a square with side \( 4 \, \text{m} \). Area of square is \( \text{side}^2 \), so original area \( = 4 \times 4 = 16 \, \text{m}^2 \).

Step2: Find new area

New area is \( 175\% \) of original. \( 175\% = 1.75 \), so new area \( = 1.75 \times 16 = 28 \, \text{m}^2 \).

Step3: Find increase in area

Subtract original from new: \( 28 - 16 = 12 \, \text{m}^2 \). Also, \( 75\% \) of original area (\( 0.75 \times 16 = 12 \)) matches the increase.

Answer:

The area of Megan’s room increased by \( 12 \, \text{m}^2 \). The original area was \( 16 \, \text{m}^2 \). \( 75\% \) of \( 16 \) is \( 12 \).