Question 1168590: The hypotenuse of a right angle triangle is 15 cm. One of the legs is 2 and half times the length of the other
leg. What is the length of the longer leg? Please use fractions when solving, not decimals, until the unknown
variable is collected to one side of the equation. Your final answer will be in decimal form.
Please HELP ME I REALLY NEED THIS THANK YOU!
Found 3 solutions by josgarithmetic, Alan3354, Theo:
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website! The one leg, (2.5)x
The other leg, x
Pythagorean Theorem Formula for your 15 cm hypotenuse:
OR since you wanted as "FRACTIONS", then
.
.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The hypotenuse of a right angle triangle is 15 cm. One of the legs is 2 and half times the length of the other
leg. What is the length of the longer leg?
=====================
x = length of shortest leg
5x/2 = longer leg
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x^2 + (5x/2)^2 = 15^2
x^2 + 25x^2/4 = 225
4x^2 + 25x^2 = 900
29x^2 = 900
x^2 = 900/29
Length of longer leg = 
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the hypotenuse is 15.
one of the legs is 2 and 1/2 * the length of the other leg.
let one of the legs be equal to x.
the other leg is then 2.5 * x
since hypotenuse squared = sum of the square of each leg, your equation becomes:
x^2 + (2.5 * x)^2 = 15^2
simplify to get x^2 + 6.25x^2 = 225
simplify further to get 7.25x^2 = 225
solve for x to get x = sqrt(225/7.25) = 5.570860145
x = 5.270860145
2.5 * x = 13.92715036
with these values, x^2 + (2.5*x)^2 = 225
sqrt(225) = 15, confirming the solution is correct.
let x = one of the legs.
the other leg is 2.5 * as large which makes the other leg equal to
that was not, however, done using fractions.
let's try again using fractions.
one leg is equal to x.
the other leg is equal to 2.5 * x = (2 + 1/2) * x = 5/2 * x
the sum of the squares of each leg is equal to the hypotenuse squared.
you get x^2 + (5/2 * x)^2 = 15^2
simplify to get x^2 + 25/4 * x^2 = 225
x^2 = 1 * x^2 and 1 = 4/4, so x^2 = 4/4 * x^2 and the equation becomes:
4/4 * x^2 + 25/4 * x^2 = 225
factor out the x^2 to get:
(4/4 + 25/4) * x^2 = 225
simplify to get:
29/4 * x^2 = 225
multiply both sides of this equation by 4/29 to get:
4/29 * 29/4 * x^2 = 4/29 * 225
simplify to get:
x^2 = 4/29 * 225
simplify to get x^2 = 900/29
solve for x to get:
x = sqrt(900/29) = sqrt(900)/sqrt(29)
sqrt(900) = 30
sqrt(29) does not appear to be a rational number and so must be left as sqrt(29).
your answer will be that x = 30/sqrt(29).
2.5 * x will be equal to 5/2 * 30/sqrt(29) = (5*30)/(2*sqrt(29)) = 75/sqrt(29).
30/sqrt(29) = 5.570860145, same as i got using decimals.
75/sqrt(29) = 13.92715036, same as i got using decimals.
the answer appears to be the same whether i used decimals or fractions, as it should.
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