If i wanted to find the triangle and the perimeter is 7x+2y units.
OPPOSITE: 2x+y
ADJACENT: 3x-5y
WHAT IS THE HYPOTHENUSE?
Please help me.
Only a right triangle has a hypotenuse. The third side of your triangle is
(7x+2y) - (2x+y) - (3x-5y) = 2x + 6y
The triangle will only be a right triangle for special values of x and y.
Oh...,ok...thank u
let the hypotenuse be h
we know
h + 3x - 5y + 2x + y = 7x + 2y
h = 2x-6y
then (2x+6y)^2 = (2x+y)^2 + (3x-5y)^2
4x^2 + 24xy + 36y^2 = 4x^2 + 4xy + y^2 + 9x^2 - 30xy + 25y^2
9x^2 - 50xy - 10y^2 = 0
Using the quadratic formula I got x = (50±√2860)/18 y
= appr. 5.75y or a negative which I will reject
So really there is an infinite number of solutions.
e.g. if y =1 then x = 5.75
side1 = 2x+y = 12.5
side2 = 3x-5y = 12.25
hypotenuse = 2x + 6y = 17.5
check: 17.5^2 = 306.25
12.5^2 + 12.25^2 = 306.31 close enough with the decimals carried.
If you let y = 2, then x = 11.5 etc.
To find the hypotenuse of a triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
In this case, we have the lengths of the two legs of the triangle as follows:
Opposite side: 2x + y
Adjacent side: 3x - 5y
To find the hypotenuse, we can substitute these values into the Pythagorean theorem:
(2x + y)^2 + (3x - 5y)^2 = (hypotenuse)^2
Expanding and simplifying the equation, we get:
4x^2 + 4xy + y^2 + 9x^2 - 30xy + 25y^2 = hypotenuse^2
Combining the like terms, the equation becomes:
13x^2 - 26xy + 26y^2 = hypotenuse^2
So, the length of the hypotenuse is the square root of the right side of the equation:
hypotenuse = √(13x^2 - 26xy + 26y^2)
Note: The perimeter you mentioned (7x + 2y) is not directly related to finding the hypotenuse length. The perimeter is the sum of all three sides of the triangle, whereas the hypotenuse is just one side of the right triangle.