how would you solve for x in a 45-45-90 triangle if the hypotenuse is 9 square root 2
I assume x is the value of the other sides, (they are equal)
the ratio of sides in a 45-45-90 triangle is 1:1:√2
so x/1 = 9√2/√2
x = 9
check: 9^2 + 9^2= h^2
h^2 = 162
h = √162 = 9√2
To solve for x in a 45-45-90 triangle, we can use the properties of these special triangles. In a 45-45-90 triangle, the two legs are congruent, and the hypotenuse is √2 times the length of either leg.
Given that the hypotenuse is 9√2, we can set up an equation to solve for the length of the legs:
Let x represent the length of each leg.
x = 9√2 / √2
Simplifying the expression on the right:
x = (9√2 / √2) * (√2 / √2)
x = (9 * 2) / 2
x = 18 / 2
x = 9
Therefore, x is equal to 9.
To solve for x in a 45-45-90 triangle, you can use the relationships between the sides of such a triangle.
In a 45-45-90 triangle, the two legs are congruent and the hypotenuse is the product of the leg length and the square root of 2.
Let's denote the length of each leg as x. Therefore, in your given triangle, the hypotenuse is 9√2.
We know that the hypotenuse is equal to the length of the leg times the square root of 2. So, we can set up the equation:
9√2 = x * √2
To solve for x, we can divide both sides of the equation by √2:
(9√2) / √2 = (x * √2) / √2
Simplifying the right side of the equation:
9 = x
Therefore, x = 9.
So, in the given triangle, the length of each leg (x) is 9.