Answer :
Answer:
The area of Andrew's tree house must be greater than or equal to 117 square feet
Step-by-step explanation:
Let
x -----> the area of Andrew's tree house in square feet
y ----> the area of Cynthia's tree house in square feet
we know that
Cynthia plans to make the area of her tree house at least 13 square feet.
The word "at least" means "greater than or equal to"
so
[tex]y\geq 13[/tex] ----> inequality A
Cynthia plans to build a tree house that is 1/3 the size of Andrew's tree house
so
Remember that
When two figures are similar, the ratio of its areas is equal to the scale factor squared
In this problem the scale factor is given
The scale factor is 1/3
The scale factor squared is 1/9
That means
The area of Andrew's tree house is 9 times greater than the area of Cynthia's tree house
or
The area of Cynthia's tree house is 9 times smaller than the area of Andrew's tree house
[tex]y=\frac{1}{9}x[/tex] ----> equation B
substitute equation B in the inequality A
[tex]\frac{1}{9}x\geq 13[/tex]
solve for x
[tex]x\geq 117\ ft^2[/tex]
so
The area of Andrew's tree house must be greater than or equal to 117 square feet
we know that Andrew's tree house is larger than Cynthia's tree house, because the problem states that Cynthia's tree house is 1/3 the size of Andrew's tree house
That means
The size of Andrew's tree house is 3 times greater than the size of Cynthia's tree house, without solving the inequality