The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle obtuse?

Question

Kymani Cox

Mathematics

25 June, 06:49

The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle obtuse?

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Answers (1)

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Izayah Weber · Answer 1

12
Step-by-step explanation:

if c^2 > a^2 + b^2

then the triangle is obtuse

since 20 is the longest side

20^2 > x^2 + (x+4) ^2

simplify

400 > x^2 + (x+4) (x+4)

FOIL

400 > (x^2) + (x^2 + 4x+4x+16)

combine like terms

400 > (2x^2 + 8x+16)

divide by 2

400/2 > 2x^2 / 2 + 8x/2 + 16/2

200 > x^2 + 4x + 8

subtract 200 from each side

0> x^2 + 4x + 8-200

0> x^2 + 4x-192

Factor

0 > (x-12) (x+16)

using the zero product property

0> x-12 0 > x+16

12>x - 16>x

x must be greater than 12

we know the longest side is 20

x+4 < 20

subtract 4

x< 16

x>12 and x < 16

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