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Sveta_85 [38]
3 years ago
13

One side of a right triangle is 8 cm shorter than the hypotenuse and 7 cm shorter than the third side. Find the lengths of the s

ides of the triangle.
Mathematics
1 answer:
Reptile [31]3 years ago
7 0

Answer:

5 cm

Step-by-step explanation:

Let the shorter side be a, longer side be b, hypotenuse be c

By Pythagorean theorem:

a² + b² = c²

a² + (a + 7)² = (a + 8)²

a² + a² + 14a + 49 = a² + 16a + 64

a² - 2a - 15 = 0

a² + 3a - 5a - 15 = 0

a(a + 3) - 5(a + 3) = 0

(a + 3)(a - 5) = 0

a = -3 or a = 5

Because a is a side length and is a positive number

a = 5

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