Question

Rachel is accenting one wall of her room by painting a pattern of squares across the wall. She wants to alternate between red squares with an area of 25 square inches and blue squares with an area of 16 square inches. Part A: Find the side length of each square. Show your work. Part B: If she has enough room to place 12 of each type of square with no space between them, how long is the wall? Explain your reasoning.

Answer 1

Answer: Part A) Length of each square is 5 inches and 4 inches respectively.

Part B) Length of wall is 108 inches.

Step-by-step explanation:

Area of red squares = 25 sq. inches

Side of red square is given by

$\text{Area of square}=Side^2\\\\Side=\sqrt{Area}\\\\Side=\sqrt{25}\\\\Side=5\ inches$

Area of blue square = 16 sq. inches

Side of blue square is given by

$\text{Area of square}=Side^2\\\\Side=\sqrt{Area}\\\\Side=\sqrt{16}\\\\Side=4\ inches$

Part A) Length of each square is 5 inches and 4 inches respectively.

Part B) If she has enough room to place 12 of each type of square with no space between them,

Length of wall is given by

$12\times (4+5)\\\\=12\times 9\\\\=108\ inches$