SOLUTION: Please help me solve this word problem. "A piece of property is in the shape of a right triangle. The longer leg is 20 meters longer than than twice the length of the shorter leg.
Question 516460: Please help me solve this word problem. "A piece of property is in the shape of a right triangle. The longer leg is 20 meters longer than than twice the length of the shorter leg. The hypotenuse is 10 meters longer than the length of the longer leg. Find the lengths of the sides of the triangular lot." I made the longer side a, the shorter side b, and the hypotenuse c. I figured out: a=2b+20 and c=a+10. Then combined them to get c=2b+20+10, then c=2b+30, and that's where I'm stuck. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! "A piece of property is in the shape of a right triangle.
The longer leg is 20 meters longer than than twice the length of the shorter leg.
The hypotenuse is 10 meters longer than the length of the longer leg.
Find the lengths of the sides of the triangular lot."
:
Using your equations
Longer leg
a = 2b+20
:
Hypot
c = a + 10
c = 2b + 30
:
a^2 + b^2 = c^2
Replacing a and c
(2b+20)^2 + b^2 = (2b+30)^2
FOIL
4b^2 + 80b + 400 + b^2 = 4b^2 + 120b + 900
Combine like terms on the left
4b^2 + b^2 - 4b^2 + 80b - 120b + 400 -900 = 0
b^2 - 40b - 500 = 0
Factors to
(b-50)(b+10) = 0
the positive solution is all we want here
b = 50 is the shorter leg
then
a = 2(50) + 20
a = 120 is the longer leg
and
c = 2(50) + 30
c = 130 is the hypotenuse
:
:
Check on a calc, enter: results = 130 confirms our solutions
