Algebra homework help

Question

Problem : David created a huge painting of a tree, which is 4.2 square yards smaller than Darrens 11.8875 square yard window. The length of the canvas is 1.25 yards larger than the tree’s length in the painting. Also, the width of the painting is 8.25 yards shorter than the tree’s length. What are the measurements of Davids painting?

Answer 1

Lots of information is given so we need to make sure we carefully read and summarize the information correctly.

Painting = Window Size – 4.2 sq yds

Painting = 11.8875 sq yds - 4.2 sq yrds = 7.6875 sq yds

“The length of the canvas is 1.25 yards larger than the tree’s length”

Let T be the length of the tree, then the length of the canvas is given by:

L=1.25T

“the width of the painting is 8.25 yards shorter than the tree’s length”

So the width of the painting is given by:

W=T-8.25

We now must use the area of a rectangle formula, since the painting is, I’m assuming, a rectangle.

Area of the Painting = Length*Width

A=L*W

Plug in what we know.

7.6875 = 1.25T(T-8.25)

Distribute

7.6875=1.25T^2-10.3125T

Subtract 7.6875 from each side

1.25T^2-10.3125T-7.6875=0

Multiply by 16 to get rid of any decimals and make it easier to factor.

20T^2-165T-123=0

Factor! Maybe use the quadratic formula. Whatever method you are familiar with.

You will get two possible values for T when factored. One will be negative and one will be positive. Since T represents a length, we toss the negative number away and let T equal the positive number. Whatever that number is (I know you can get it on your own!), plug it into the formulas we found for length and width earlier:

L=1.25T = ?

W=T-8.25= ?

Whew, that was a lot of work!