algebra 2 math question?

Question

the foundation of a house is in the shape of 2 adjacent squares, as show. the perimeter of the foundation is 80 meters and the area is 325 square meters. Find the length of a side of each square
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WORK PLEASE? :)

Answer 1

HAHA!! This exact same question was posted by someone else earlier, and I answered it!!! Are you the same student, or just in a different class?

********* I went and found it from the other screenname that asked it ... here's your answer ************

You have to set up 2 equations to answer this problem. First, you have the area of both squares adding up to 325. Then you have the total perimeter equalling 80.

if x = length of side of smaller square and
if y = length of side of larger square, then ...

x² + y² = 325. (the area part)

Now, with the two squares butted up next to each other, the 'y' square would be taller. So you have 3 sides of the y exposed fully, 3 sides of the x exposed fully, and then the little piece on the 4th side of the y square that is exposed (because the x square next to it isn't as tall). Therefore you have ...

3y + 3x + (y-x) = 80

The y-x here is the amount left on the y side that is partially covered by the x. The equation above can be reduced to ...

4y + 2x = 80 ---- and reduced again to
2y + x = 40 ----- (div. all parts by 2).

Now you have a system of equations to solve. Substitution is the most obvious approach .. so I need one of the equations to isolate a single variable... I chose the bottom one ..

2y + x = 40
2y + x - 2y = 40 - 2y
x = 40 - 2y <--- I can take this and substitue into the first equ.

That makes ...

(40 - 2y)² + y² = 325.

This equation can be expanded and solved using the quadratic formula or the reverse foil method. I will expand it a bit for you here....

(1600 - 160y + 4y²) + y² = 325
5y² - 160y + 1600 = 325 ---- divide all parts by 5
y² - 32y + 320 = 65 ---- get everything equal to 0.
y² - 32y + 255 = 0

You can solve this equation however you choose to get an answer. I will leave that for you, but warning! You will get 2 values for y that solve this equation. That's ok because there are actually two combinations of numbers that will work in this scenario!!!

Good luck with the rest of your homework. I hope what I wrote helps!!

Answer 2

15^2 + 10^2 = 325

15 + 15 + 5 + 10 + 10 + 25 = 80

Big square the sides are 15

Little square the sides are 10