SOLUTION: one leg of a right triangle is 2 cm longer than the other leg, hypotenuse is 7 cm longer than the shorter leg. find the lengths of three sides of the right triangle

Algebra ->  Triangles -> SOLUTION: one leg of a right triangle is 2 cm longer than the other leg, hypotenuse is 7 cm longer than the shorter leg. find the lengths of three sides of the right triangle      Log On


   

Question 1207016: one leg of a right triangle is 2 cm longer than the other leg, hypotenuse is 7 cm longer than the shorter leg. find the lengths of three sides of the right triangle
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Show what is described arranged in whatever way works.
one leg                        x+2
other leg (shorter leg)        x
hypotenuse                     x+7

If this is a reasonable right triangle then x%5E2%2B%28x%2B2%29%5E2=%28x%2B7%29%5E2 and you solve this...

checking with T. Inequality Thm.
(adjusted)
x+2+x>x+7
2x>x+5
x>5
-
x+2+x+7>x
x>-9
-
x+x+7>x+2
x>-5
-
all seem ok

Solve Equation
x%5E2%2Bx%5E2%2B4x%2B4=x%5E2%2B14x%2B49
x%5E2-10x=45
x%5E2-10x-45=0
x=%2810%2B-+sqrt%28100-4%2A1%28-45%29%29%29%2F2
x=%2810%2B-+sqrt%28280%29%29%2F2
x=%2810%2B-+sqrt%2810%2A4%2A7%29%29%2F2
x=%2810%2B-++2%2Asqrt%2870%29%29%2F2
x=5%2B-+sqrt%2870%29
x=5%2Bsqrt%2870%29

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

a = x = shorter leg
b = x+2 = longer leg
c = x+7 = hypotenuse

The Pythagorean Theorem
a^2+b^2 = c^2
leads to
x^2+(x+2)^2 = (x+7)^2

Expand everything out and get everything to one side to end up with this
x^2 - 10x - 45 = 0

Use of the quadratic formula will lead to:
x = 5 + sqrt(70) = 13.3666 or x = 5 - sqrt(70) = -3.3666
The decimal values are approximate.
The negative solution is tossed out since we cannot have a negative side length.

x = 13.3666 leads to,
x+2 = 13.3666+2 = 15.3666
x+7 = 13.3666+7 = 20.3666

Summary
The sides of the right triangle are
a = 13.3666
b = 15.3666
c = 20.3666
Each value is approximate.

Check:
a^2+b^2 = c^2
13.3666^2+15.3666^2 = 20.3666^2
414.79839112 = 414.79839556
The two sides aren't an exact match, but they're very close.
We have a bit of rounding error.
The decimal portion "79839" matches up at least.

Another way to check:
a^2+b^2 = c^2
a^2+b^2-c^2 = 0
13.3666^2+15.3666^2-20.3666^2 = 0
-0.00000444 = 0
Note the first five decimal digits are 0 to indicate we have those decimal digits matching in the previous check section (the "79839" portion).