SOLUTION: The diagonal on a right triangle is 50 feet. The longer side is 10 feet more than the shorter side. What are the lengths of the sides?
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Question 1062117: The diagonal on a right triangle is 50 feet. The longer side is 10 feet more than the shorter side. What are the lengths of the sides? Answer by addingup(3677) (Show Source):
You can put this solution on YOUR website! The diagonal is the hypotenuse. Pythagoras says:
a^2 = b^2+c^2
50^2 = x^2+(x+10)^2
2500 = x^2+(x+10)^2
let's flip the equation to get the unknown on the left:
x^2+(x+10)^2 = 2500
Expand out terms of the left hand side:
2x^2+20x+100 = 2500
Divide both sides by 2:
x^2+10x+50 = 1250
x^2+10x = 1200
x^2+10x+25 = 1225
(x+5)^2 = 1225
x+5 = 35 or x+5 = -35
x = 30 or x = -40
We don't need a negative number, so let's try 30:
30^2+40^2 = 50^2 Correct!
:
John
