SOLUTION: How many right triangles have a hypotenuse that measures 4x + 5 inches and legs that measure 3x + 13 inches and x inches? What are the dimensions of the triangle(s)? Let me se

Algebra ->  Pythagorean-theorem -> SOLUTION: How many right triangles have a hypotenuse that measures 4x + 5 inches and legs that measure 3x + 13 inches and x inches? What are the dimensions of the triangle(s)? Let me se      Log On


   

Question 1207407: How many right triangles have a hypotenuse that measures 4x + 5 inches and legs that measure 3x + 13 inches and x inches? What are the dimensions of the triangle(s)?

Let me see.

I must use a^2 + b^2 = c^2.


Yes?

My set up:

(3x + 13)^2 + x^2 = (4x + 5)^2

If this is correct, what does the value of x represent in this case?
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Looks good so far.

(3x + 13)^2 + x^2 = (4x + 5)^2
(3x + 13)(3x + 13) + x^2 = (4x + 5)(4x + 5)
9x^2+39x+39x+169 + x^2 = 16x^2+20x+20x+25
10x^2+78x+169 = 16x^2+40x+25
0 = 16x^2+40x+25-(10x^2+78x+169)
0 = 16x^2+40x+25-10x^2-78x-169
0 = 6x^2-38x-144
6x^2-38x-144 = 0

From here use the quadratic formula.
I'll let the student finish up.