The hypotenuse of a right triangle is 7 feet long. One leg of the triangle is 5 feet longer then the other leg. Find the sum of the lengths of the two legs of the right triangle.
Note: sqrt refers to the square root.
The answers are:
a. sqrt(329) feet
b. sqrt(313) feet
c. sqrt(233) feet
d. sqrt(217) feet
e. sqrt(89) feet
f. sqrt(73) feet
g. sqrt(41) feet
h. None of these
2007-12-08 10:20:15 · 3 answers · asked by Sheena 1 in Science & Mathematics ➔ Mathematics
Use Pythagoras:
7² = x² + (x + 5)²
49 = x² + x² + 10x + 25
2x² + 10x - 24 = 0
x² + 5x - 12 = 0
x = [-5 +/- √(25 + 48)] / 2 = 1.772
x + 5 = 6.772
Sum of 2 legs = 8.544 = √72.999 (answer f)
Proof: 1.772² + 6.772² = 48.999 = 7²
2007-12-08 10:48:56 · answer #1 · answered by Joe L 5 · 0⤊ 0⤋
Pythagoras is your friend.
The sum of the sides squared = the hypotenuse squared.
So let x represent the short side.
x^2 + (x+5)^2 = 7^2
x^2 + x^2 + 10x + 25 = 49
2x^2 + 10x = 49-25
Restate as quadratic:
2x^2 + 10x - 24 = 0
Extract common factor:
2(x^2 + 5x - 12) = 0
Cannot factor as binomial:
Use quadratic formula:
2007-12-08 18:48:20 · answer #2 · answered by Robert S 7 · 0⤊ 0⤋
Let one side be x
Other side is x+5
Using Pythagoras
x^2 +(x+5)^2 = 49
2x^2 + 10x -24=0
x^2 +5x -12=0
x= -5 +- sqr(73) / 2
ignore negative answer
x={ sqr73 -5}/2
x+5 = {sqr 73+5}/2
Sum of sides = sqr(73) feet
2007-12-08 18:41:32 · answer #3 · answered by Anonymous · 0⤊ 0⤋