Let x = one of the legs.
Then, the other leg = x + 3.
Ed will use the Pythagorean Theorem to find the hypotenuse.
So, let a = x one leg. Let b= x + 3 the other leg. And, let c = 15 the hypotenuse.
The Pythagorean Theorem is:
c^2 = a^2 + b^2, where a and b are the legs and c is the hypotenuse.
We have:
15^2 = x^2 + (x + 3)^2
225 = x^2 + x^2 + 6x + 9
Rearranging:
2x^2 + 6x - 216 = 0
Divide by 2:
x^2 + 3x - 108 = 0
Solve by factoring:
(x - 9)(x + 12) = 0
So, x = 9 and x = -12. (x = -12 is not a valid answer.)
x = 9
x + 3 = 12
Conclusion: The legs of the right triangle are 9 inches and 12 inches.
Eddie-G…
<span>1 gallon is equal to 3.78541 liters. Therefore, a half gallon would be equal to about 1.89271 liters. Thus, a 2 liter bottle holds more. </span>
3x = 72 /3
X = 24
X^3 = 72
X = (72)^(1/3)
X= 4.160167646
Since the triangles are similar, the ratio of each side in one triangle to
the corresponding side in the other one is always the same number.
We know what one pair of sides is ... 3.5 and 7 ... so we know that
each side in the first triangle is 1/2 as long as the corresponding side
in the other one.
So we can say with assurance that ...
y = 1/2 (x + 4)
and
x = 1/2 (3y) .
That's all the intelligence required for this problem. The rest is just algebra,
and I should not need to go through all the routine misery for you here.
When you solve this pair of equations slowly, carefully, and accurately,
you'll find that the sides of the triangles are ...
3.5, 8, 12
and
7, 16, 24 .
