SOLUTION: A square and a triangle have the same area. The base of the triangle is 3 ft. more than the side length of the square. The height of the triangle is 1 ft. less than the base of the

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Question 1021942: A square and a triangle have the same area. The base of the triangle is 3 ft. more than the side length of the square. The height of the triangle is 1 ft. less than the base of the triangle. What is the side length of the square? What are the base and height of the triangle?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, side length of the square
b, base of the triangle
h, height of the triangle

system%28x%5E2=%281%2F2%29bh%2Cb=3%2Bx%2Ch=-1%2Bb%29

You can solve this system for all three variables, but you are interested in b and h.

Here is a possible start.
b=h%2B1
-
b=x-3
h%2B1=x-3
x-3=h%2B1
x=h%2B1%2B3
x=h%2B4
-
Substitute this into the area equation:
%28h%2B4%29%5E2=%281%2F2%29bh
But you ALSO have a relation between b and h which you can substitute...
highlight%28%28h%2B4%29%5E2=%281%2F2%29%28h%2B1%29%2Ah%29
which is an equation in only one unknown variable, h. Simplify and solve this for h.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

A square and a triangle have the same area. The base of the triangle is 3 ft. more than the side length of the square. The height of the triangle is 1 ft. less than the base of the triangle. What is the side length of the square? What are the base and height of the triangle?
Let the length of one side of the square, be S

Then area of square = S%5E2

Also, length of base of triangle = S + 3, and height = S + 3 – 1, or S + 2

Area of triangle = %281%2F2%29bh, or %281%2F2%29%28S+%2B+3%29%28S+%2B+2%29, or %28%28S+%2B+3%29%28S+%2B+2%29%29%2F2, or %28S%5E2+%2B+5S+%2B+6%29%2F2

We then get: S%5E2+=+%28S%5E2+%2B+5S+%2B+6%29%2F2

2S%5E2+=+S%5E2+%2B+5S+%2B+6 -------- Cross-multiplying

2S%5E2+-+S%5E2+-+5S+-+6+=+0

S%5E2+-+5S+-+6+=+0

(S - 6)(S + 1) = 0  

S, or one side of square = highlight_green%28matrix%281%2C2%2C6%2C+feet%29%29 

Length of triangle’s base: 6 + 3, or highlight_green%28matrix%281%2C2%2C9%2C+feet%29%29

Height = 6 + 2, or highlight_green%28matrix%281%2C2%2C+8%2C+feet%29%29