Answer :
Answer:
- shortest: 3 ft
- other: 4 ft
Step-by-step explanation:
The right triangle with hypotenuse 5 that has legs that differ by 1 is the 3-4-5 right triangle. The legs are 3 ft and 4 ft.
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Alternate solution
If you have never heard of a 3-4-5 right triangle, you can figure the leg lengths algebraically using the Pythagorean theorem. Let x represent the length of the "other" leg. Then the shortest is (x-1). The Pythagorean theorem tells you ...
5^2 = (x)^2 +(x -1)^2
25 = 2x^2 -2x +1
12 = x^2 -x = x(x -1)
Factors of 12 that differ by 1 are 3 and 4 or -3 and -4. We want x to be positive, so the value of interest is x=4
The "other" leg is 4 ft; the shortest leg is 3 ft.
Answer:
3 ft, 4 ft
Step-by-step explanation:
Represent the length of the shortest leg using x. Then the other leg length is x + 1. Applying the Pythagorean Theorem,
x^2 + (x + 1)^2 = 5^2, or
x^2 + x^2 + 2x + 1 = 25, or
2x^2 + 2x - 24 = 0.
Reducing this, we get x^2 + x - 12 = 0, or (x + 4)(x - 3) =0.
Solving for x: x + 4 = 0 => x = -4; also x - 3 = 0 => x = 3
Since we're measuring length, let's omit x = -4 and focus on x = 3.
Shortest leg is 3 ft long; other leg length is 3 + 1 ft, or 4 ft, long.