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Fed [463]
2 years ago
5

The length of the long leg of a right triangle is 16 inches more than four times of the shorter leg. The length of the hypotenus

e is 17 inches more than four times the length of the shorter leg. Find the side lengths of the triangle.
Mathematics
1 answer:
Galina-37 [17]2 years ago
8 0

Answer:

The side lengths of the triangle, in order, are 11 inches, 60 inches, 61 inches.

Step-by-step explanation:

Let the shorter leg be x, the longer leg, y and the hypotenus, z.

y = 16 + 4x

z = 17 + 4x

By Pythagoras rule,

z^2 = x^2 + y^2

(17+4x)^2 = x^2 + (16+4x)^2

that is,

x^2 - 8x - 33 = 0  (A quadratic equation)

By factorising,

(x+3)(x-11)=0

either x = -3 or x = 11.

But length cannot be negative. Hence, -3 is dicarded.

x = 11 inches

y = 16 + 4x = 60 inches

z = 17 + 4x = 61 inches

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