Problema Solution
A dorm room desktop organizer is roughly in the shape of a right triangle. The height and base are the solution to the equation x^2+440=42x+8. Find the hypotenuse.h
Answer provided by our tutors
let
a = height, a>0
b = the base, b>0
c = the hypotenuse, c >0
using the Pythagorean Theorem we have:
c^2 = a^2 + b^2
on the other hand: a^2 + b^2 = (a + b)^2 - 2ab thus
c^2 = (a + b)^2 - 2ab
since a and b are the solutions to the equation x^2+440=42x+8 or this is equivalent to: x^2 - 42 x+432=0
using Vieta's formulas we know that:
a + b = -(-42)
a + b = 42
ab = 432
plug a + b = 42 and ab = 432 into c^2 = (a + b)^2 - 2ab:
c^2 = 42^2 - 2*432
c^2 = 900
c = 30
the hypotenuse is 30.