SOLUTION: The hypotenuse of a triangle rectangle is 19.5 ft long. If the length of each leg increased 4.5 ft, the hypotenuse would increase by 6 ft. Calculate both leg lengths of the f

Algebra ->  Pythagorean-theorem -> SOLUTION: The hypotenuse of a triangle rectangle is 19.5 ft long. If the length of each leg increased 4.5 ft, the hypotenuse would increase by 6 ft. Calculate both leg lengths of the f      Log On


   

Question 1086275: The hypotenuse of a triangle rectangle is 19.5 ft long.
If the length of each leg increased 4.5 ft, the hypotenuse would increase by 6 ft.
Calculate both leg lengths of the first triangle.
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What is a "triangle rectangle" ?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a triangle rectangle : I guess you have rectangle divided into two triangle


let’s hypotenuse be c, and legs a and b

since your triangle is right angle triangle, we have
c%5E2=a%5E2%2Bb%5E2
19.5+%5E2=a%5E2%2Bb%5E2
380.25=a%5E2%2Bb%5E2.....solve for b
b%5E2=380.25-a%5E2
b=sqrt%28380.25-a%5E2%29...........eq.1
If the length of each leg increased 4.5 ft, the hypotenuse would increase by 6 ft.
%2819.5%2B6%29+%5E2=%28a%2B4.5%29%5E2%2B%28b%2B4.5%29%5E2
%2825.5%29+%5E2=+a%5E2%2B9a%2B20.25%2Bb%5E2%2B9b%2B20.25
650.25=+a%5E2%2B9a%2Bb%5E2%2B9b%2B40.5
650.25-40.5=+a%5E2%2B9a%2Bb%5E2%2B9b
609.75=+a%5E2%2B9a%2Bb%5E2%2B9b.......substitute b
609.75=+a%5E2%2B9a%2B%28sqrt%28380.25-a%5E2%29%29%5E2%2B9%2Asqrt%28380.25-a%5E2%29
609.75=+a%5E2%2B9a%2B380.25-a%5E2%2B9%2Asqrt%28380.25-a%5E2%29
609.75=+9a%2B380.25%2B9%2Asqrt%28380.25-a%5E2%29
609.75-380.25=+9a%2B9%2Asqrt%28380.25-a%5E2%29
229.5=+9%28a%2Bsqrt%28380.25-a%5E2%29%29
229.5%2F9=+a%2Bsqrt%28380.25-a%5E2%29
25.5-a=sqrt%28380.25-a%5E2%29....square both sides
%2825.5-a%29%5E2=%28sqrt%28380.25-a%5E2%29%29%5E2

650.25-51a%2Ba%5E2=380.25-a%5E2%29

a%5E2%2Ba%5E2-51a%2B650.25-380.25=0

2a%5E2-51a%2B270=0
%28a+-+18%29+%282+a+-+15%29+=+0
%28a+-+18%29+=+0=>a=18ft
or
+%282+a+-+15%29+=+0=>a=7.5ft
now find b
b=sqrt%28380.25-a%5E2%29...........eq.1=>a=18
b=sqrt%28380.25-18%5E2%29
b=sqrt%28380.25-324%29
b=7.5ft

b=sqrt%28380.25-a%5E2%29...........eq.1=>a=7.5
b=sqrt%28380.25-7.5%5E2%29
b=sqrt%28324%29
b=18ft
so, you can choose a=18 and b=7.5ft or vice versa