SOLUTION: Directions: Make a sketch for each problem(optional). Approximathe each square root to the nearest hundreth. A calculator may be helpful. Problem: A right triangle has sides who

Question 190973This question is from textbook Algebra Structure and Method book 1
: Directions: Make a sketch for each problem(optional). Approximathe each square root to the nearest hundreth. A calculator may be helpful.
Problem: A right triangle has sides whose length in feet are consecutive even integers. Determine the length of each side. This question is from textbook Algebra Structure and Method book 1

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Problem: A right triangle has sides whose length in feet are consecutive even integers. Determine the length of each side.
.
Let x = smallest even integer (1st leg)
then
x+2 = 2nd leg
x+4 = hypotenuse
.
If it is a "right triangle" we can apply Pythagorean theorem:
x^2 + (x+2)^2 = (x+4)^2
x^2 + (x+2)(x+2) = (x+4)(x+4)
x^2 + x^2+4x+4 = x^2+8x+16
2x^2+4x+4 = x^2+8x+16
x^2+4x+4 = 8x+16
x^2-4x+4 = 16
x^2-4x-12 = 0
(x-6)(x+2) = 0
x = {-2,6}
We can toss out the negative solution leaving us with:
x = 6 feet
.
The three sides are then:
6 feet, 8 feet, and 12 feet

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