Ociel has designed a square mural that measures 10 feet on each side. Bill has also designed a square mural, but his measures y feet shorter on each side.
a. Write an expression to represent the area of Bill's mural: (10-2y)(10-2y)
b. How much smaller than Ociel's mural is Bill's mural? Explain
One side of Bill's mural is 10/(10-2y) times smaller than Ociel's. In total, his mural is (10/(10-2y))^2 times smaller
To find the area of a square mural, you need to multiply the length of one side by itself. For Ociel's mural, each side is 10 feet, so its area is 10 * 10 = 100 square feet.
For Bill's mural, the length of each side is 10 feet minus y feet. So, the expression to represent the area of Bill's mural is (10-2y)(10-2y). We subtract y twice because the length and width of the mural are both reduced by y feet.
To find out how much smaller Bill's mural is compared to Ociel's mural, you subtract the area of Bill's mural from the area of Ociel's mural. Therefore, we have:
Ociel's mural area - Bill's mural area = 100 sq.ft - (10-2y)(10-2y)
You can simplify further by expanding the expression (10-2y)(10-2y) using the distributive property:
100 sq.ft - (10-2y)(10-2y) = 100 sq.ft - (100 - 20y - 20y + 4y^2)
Simplifying and combining like terms:
100 sq.ft - (100 - 40y + 4y^2) = 100 sq.ft - 100 + 40y - 4y^2
Now, you can see that both 100 sq.ft and -100 cancel each other out, leaving us with:
40y - 4y^2
Therefore, Bill's mural is 40y - 4y^2 square feet smaller than Ociel's mural.
a. The expression to represent the area of Bill's mural would be:
(10-2y)(10-2y)
b. Bill's mural is smaller than Ociel's mural by the difference in area between the two murals. The area of Ociel's mural is 10*10 = 100 square feet. To find the difference in the area, we can subtract the area of Bill's mural from the area of Ociel's mural. Therefore, the difference in area is:
100 - (10-2y)(10-2y) square feet.