SOLUTION: One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 28. Find the lengths of all three sides, to three decimal places

Algebra ->  Triangles -> SOLUTION: One of the legs of a right triangle is twice as long as the other, and the perimeter of the triangle is 28. Find the lengths of all three sides, to three decimal places      Log On


   

Question 1074153: One of the legs of a right triangle is twice as long as the other, and the perimeter of the
triangle is 28. Find the lengths of all three sides, to three decimal places
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Legs, x and 2x
longest side, r


x%2B2x%2Br=28
3x%2Br=28


x%5E2%2B%282x%29%5E2=r%5E2
x%5E2%2B4x%5E2=r%5E2
5x%5E2=r%5E2

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5x%5E2=%2828-3x%29%5E2
5x%5E2=28%5E2-6%2A28x%2B9x%5E2
0=28%5E2-6%2A28x%2B4x%5E2
x%5E2-42x%2B7%2A28=0

x=%2842%2B-+sqrt%28980%29%29%2F2
x=%2842%2B-+sqrt%2849%2A2%2A2%2A5%29%29%2F2
x=%2842%2B-+14sqrt%285%29%29%2F2
x=21%2B-+7%2Asqrt%285%29


The MINUS form:
x is 5.348, 2x is 10.695, r is 11.956
check: 5.348^2+10.695^2=11.956^2
142.98 = 142.95

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LEG: highlight%28x=21-7sqrt%285%29%29
.
Other LEG: highlight%282x=42-14%2Asqrt%285%29%29
.
r=28-%2821-7sqrt%285%29%29-%2842-14sqrt%285%29%29
HYPOTENUSE: highlight%28r=-35%2B21%2Asqrt%285%29%29, about 11.957
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The PLUS form:
x is 36.6.... No. This does not work.