SOLUTION: I know the hypotenuse is 25 in. I know the base to height ratio is 3 : 4. How do I find the lenght of base and height?

Algebra ->  Triangles -> SOLUTION: I know the hypotenuse is 25 in. I know the base to height ratio is 3 : 4. How do I find the lenght of base and height?      Log On


   

Question 279808: I know the hypotenuse is 25 in. I know the base to height ratio is 3 : 4. How do I find the lenght of base and height?
Found 2 solutions by JBarnum, richwmiller:
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E2%2Bb%5E2=c%5E2
a%5E2%2Bb%5E2=25%5E2
a%5E2%2Bb%5E2=625
list same ratios and put in the equation a%5E2%2Bb%5E2=c%5E2
to find equivalent ratios multiply both numbers by the same number
3:4 3%5E2%2B4%5E2=9%2B16=25
6:8 (i multiplied 3:4 by 2) 6%5E2%2B8%5E2=36%2B64=100
9:12 (i multiplied 3:4 by 3) 9%5E2%2B12%5E2=81%2B144=225
12:16 (i multiplied 3:4 by 4) 12%5E2%2B16%5E2=144%2B256=400
15:20 (i multiplied 3:4 by 5)15%5E2%2B20%5E2=225%2B400=625
hey we found 625 so the lengths have to be 15 and 20

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(3x)^2+(4x)^2=25^2
9x^2+16x^2=625
25x^2=625
x^2=25
x=5
3x=15 base
4x=20 height
the base and height are 15 and 20