Solve.
-A lot is in the shape of a right triangle. The shorter leg measures 60 m. The hypotenuse is 20 m longer than the length of the longer leg. How long is the longer leg?
A)100 m
B)60 m
C)80 m
D)120 m

Question

Quizplus · Accepted Answer

Let x be the length of the longer leg. Then, using the Pythagorean theorem, we have:
(60)^2 + x^2 = (x+20)^2
Simplifying this equation, we get:
3600 + x^2 = x^2 + 40x + 400
Subtracting x^2 from both sides, we get:
3600 = 40x + 400
Subtracting 400 from both sides, we get:
3200 = 40x
Dividing both sides by 40, we get:
x = 80
Therefore, the longer leg is 80 meters long, which corresponds to choice C. Let x be the length of the longer leg. Using the Pythagorean theorem, we can set up the equation: 
60^2 + x^2 = (x+20)^2 
Expanding the right side: 
3600 + x^2 = x^2 + 40x + 400 
Simplifying: 
40x = 3200 
x = 80 
Therefore, the longer leg is 80 meters long.

Solve. -A Lot Is in the Shape of a Right Triangle