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.




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Answer 1

Answer:

A: Side length of red square = 5 inches

Side length of blue square = 4 inches

B: Length of wall = 108 inches.

Step by step explanation:

A: Since we know that all sides of a square has equal length and area of square is square of its side length. We can find side length of our given squares by taking square root of area of our squares.

We have been given that area of red squares is 25 square inches. Let us take square root of 25 to find side length of red square.

$\text{Side length of red square}=\sqrt{25\text{ inches}^{2}}$

$\text{Side length of red square}=5\text{ inches}$

Therefore, side length of red square will be 5 inches.

Now let us find side length of blue square by taking square root of 16 as area of blue square is 16 square inches.

$\text{Side length of blue square}=\sqrt{16\text{ inches}^{2}}$

$\text{Side length of blue square}=4\text{ inches}$

Therefore, side length of blue square will be 4 inches.

B: Since there is no space between the squares, we can find the length of the wall by adding the lengths of all the squares.

We have been given that Rachel can place 12 of each type of square. Let us find length of wall by multiplying 12 with sum of side length of both squares.

$\text{Length of wall}=12\cdot(5+4)$

$\text{Length of wall}=12\cdot(9)$

$\text{Length of wall}=108$

Therefore, length of wall will be 108 inches.