Question

Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Cynthia plans to make the area of her tree house at least 13 square feet. Write and solve an inequality to find the area of Andrew's tree house. Let x be the area of Andrew's tree house. Describe how you know which tree house is larger without solving the inequality.

Answer 1

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

$y\geq 13$ ----> 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

$y=\frac{1}{9}x$ ----> equation B

substitute equation B in the inequality A

$\frac{1}{9}x\geq 13$

solve for x

$x\geq 117\ ft^2$

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