217k views
5 votes
The shorter leg of a right triangle is 14 feet less than the other leg. Find the length of the two legs of the hypotenuse is 25 feet.

2 Answers

2 votes

Answer: 9 ft, 23 ft

Explanation:

We know the Pythagorean Theorem is a²+b²=c². Since one leg is 14 less than the other leg, we can use x-14 and the other leg would be x. We can plug these into the Pythagorean Theorem with the given hypotenuse.

(x-14)²+x²=25²

(x²-28x+196)+x²=625

2x²-28x+196=625

2x²-28x-429=0

When we solve for x, we get
x=(14+√(1054) )/(2) and
x=(14-√(1054) )/(2).

Note, since we rounded to 23, the hypotenuse isn't exactly 25, but it gets very close.

User Prashin Jeevaganth
by
7.5k points
7 votes

Answer:

9.233 ft, 23.233 ft

Explanation:

If the shorter leg is x, then the longer leg is x+14 and the Pythagorean theorem tells you ...

x^2 + (x +14)^2 = 25^2

2x^2 +28x +196 = 625

x^2 +14x = 214.5

x^2 +14x +49 = 263.5

(x +7)^2 = 263.5

x = -7 +√263.5 ≈ 9.23268

The two leg lengths are √263.5 ± 7 feet, {9.23 ft, 23.23 ft}.

The shorter leg of a right triangle is 14 feet less than the other leg. Find the length-example-1
User Osyan
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories