The length of the hypotenuse of a right triangle is 2m more than the longer leg. The longer leg is 7m longer than the shorter leg. Find the perimeter of the triangle. ( please explain as you go)
If the sides in order of length are a,b,c then
b = a+7
c = b+2 = a+9
a^2+b^2 = c^2
a^2+(a+7)^2 = (a+9)^2
a=8, b=15, c=17
I think you can take it from there, right?
Yes thank you so much!!
To find the perimeter of the right triangle, we need to determine the lengths of all three sides.
Let's denote:
- The longer leg as "L"
- The shorter leg as "S"
- The hypotenuse as "H"
We are given two pieces of information:
1) The length of the hypotenuse is 2 meters more than the longer leg: H = L + 2
2) The longer leg is 7 meters longer than the shorter leg: L = S + 7
Our first step is to write an equation using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Applying this theorem, we have: H^2 = L^2 + S^2
Substituting the given information into the equation, we have:
(L + 2)^2 = L^2 + (S + 7)^2
Expanding and simplifying the equation:
L^2 + 4L + 4 = L^2 + S^2 + 14S + 49
Now we can simplify further by canceling out the common terms "L^2" on both sides of the equation:
4L + 4 = S^2 + 14S + 49
Next, let's isolate the "L" term on one side:
4L = S^2 + 14S + 49 - 4
4L = S^2 + 14S + 45
To find the values of "L" and "S" that satisfy the equation, we need additional information or constraints. Can you provide any information regarding the relationship of "L" and "S"?