The longer leg of a right triangle is 3 more than the shorter leg. The Hypotenuse is 6 more than the shorter leg. If the perimeter of the triangle is 36, find the length of each side of the right triangle. [ Only an algebraic solution will be accepted ]
not just the answer , please
shorter leg --- x
longer leg ---- x+3
hypotenus ---- x+6
x+x+3+x+6 = 36
3x = 27
x = 9
short leg = 9
longer leg = 12
hypotenuse = 15
check to make sure it is right-angled:
9^2 + 12^2 = 225
15^2 = 225
all is good.
Let's denote the lengths of the shorter leg, longer leg, and the hypotenuse as x, x+3, and x+6 respectively.
According to the given information, the perimeter of the triangle is 36. So, we can set up the equation as follows:
x + (x+3) + (x+6) = 36
Simplifying the equation, we have:
3x + 9 = 36
Removing 9 from both sides of the equation:
3x = 27
Now, divide both sides of the equation by 3:
x = 9
Therefore, the length of the shorter leg is 9 units.
To find the lengths of the other two sides, we can substitute the value of x back into the initial expressions:
The longer leg = 9 + 3 = 12 units
The hypotenuse = 9 + 6 = 15 units
So, the lengths of the sides of the right triangle are 9 units, 12 units, and 15 units.
To solve this problem algebraically, let's assume that the shorter leg of the right triangle is represented by the variable x.
According to the problem, the longer leg is 3 more than the shorter leg, so it can be represented as (x + 3).
The hypotenuse is given as 6 more than the shorter leg, so it can be represented as (x + 6).
The perimeter of the triangle is the sum of all three sides, which is given as 36.
So, we can write the equation:
Shorter leg + Longer leg + Hypotenuse = Perimeter
x + (x + 3) + (x + 6) = 36
Now, let's simplify the equation and solve for x:
3x + 9 = 36
Subtracting 9 from both sides:
3x = 27
Dividing both sides by 3:
x = 9
So, the shorter leg of the triangle is 9.
Now, we can substitute this value back into the other expressions:
Longer leg = (x + 3) = 9 + 3 = 12
Hypotenuse = (x + 6) = 9 + 6 = 15
Therefore, the lengths of the sides of the right triangle are:
Shorter leg = 9
Longer leg = 12
Hypotenuse = 15