Eli R. answered • 05/08/20

"You SHALL pass." - Gandalf, maybe

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!