The hypotenuse of a right triangle is 25m long. The length of one leg is 10m less than twice the other. Find the length of each leg.
Can you tell me how to set this up? I can do the math from there.
a^2+b^2=c^2
x^2+(2x-10)^2=25^2
4x^7-6=-2
Sure! To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs).
Let's denote the lengths of the legs as x and y. We are given that the hypotenuse is 25m, so we have:
Hypotenuse = 25m
One leg = x
Other leg = y
We are also given that the length of one leg is 10m less than twice the other, which we can write as:
x = 2y - 10
Now we can use the Pythagorean theorem to set up an equation. According to the theorem, we have:
(Length of hypotenuse)^2 = (Length of one leg)^2 + (Length of other leg)^2
Substituting the given values, we get:
25^2 = x^2 + y^2
We can also substitute the expression for x from the second given condition:
25^2 = (2y - 10)^2 + y^2
Simplifying this equation will give us a quadratic equation that we can solve to find the values of x and y.