55 POINTS!!! The hypotenuse of a right triangle is 5cm more than 4 times the length of the shortest leg. The longer leg and the hypotenuse are consecutive integers. Find all lengths.
1 answer:
Answer:
Short leg is 9.
Hypotenuse is 41.
Long leg is 40.
Step-by-step explanation:
Shortest leg is x.
Hypotenuse is (4x + 5).
Longer leg is shorter than hypotenuse, and they are consecutive numbers,
so longer leg is (4x + 5 - 1) = (4x + 4).
Using Pythagorean theorem
x² + (4x + 4)² = (4x + 5)²
x² + 16x² + 2*4x*4 + 4² = 16x² + 2*4x*5 + 5²
x² + 32x + 16 = 40x + 25
(x - 4)² = 5²
x - 4 = 5 or x - 4 = - 5
x = 9 , or x = - 1
Leg cannot be negative.
So, short leg is 9.
Hypotenuse (4x+5) = (4*9 + 5) = 41
Long leg is 41 - 1 = 40
Check:
9² + 40² = 41²
1681 = 1681 True
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