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