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Help asap............ It is the topic of pythegoras theorem ​

Help asap............ It is the topic of pythegoras theorem ​-example-1
User Timmkrause
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1 Answer

5 votes

Answer:

x = 5

Explanation:

since you know that Pythagoras is to be used, simply apply it.

c² = a² + b²

c is the Hypotenuse (the baseline = the side opposite of the 90° angle), a and b are the legs.

so, we have

(x + 8)² = x² + (x + 7)²

x² + 16x + 64 = x² + x² + 14x + 49

16x + 64 = x² + 14x + 49

64 = x² - 2x + 49

0 = x² - 2x - 15

we need to solve this quadratic equation.

you know, the general solution for a quadratic equation

0 = ax² + bx + c

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -2

c = -15

x = (2 ± sqrt((-2)² - 4×1×-15))/(2×1) =

= (2 ± sqrt(4 + 60))/2 = (2 ± sqrt(64))/2 =

= (2 ± 8)/2 = (1 ± 4)

x1 = 1 + 4 = 5

x2 = 1 - 4 = -3

since a negative number for the length of a side does not make any sense, it means our valid solution is

x = 5

User Mike Vella
by
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