leg xy of the right triangle is twice as long as leg yz. if the area of the triangle is 36cm to the second power what is the length icm of xy?
To solve this problem, we can use the formula for the area of a right triangle:
Area = (base * height) / 2
Let's assign variables to the lengths of the legs:
Let "x" be the length of leg YZ.
Since leg XY is twice as long as leg YZ, we can say that leg XY is 2x.
The area of the triangle is given as 36 cm²:
36 = (x * 2x) / 2
36 = (2x²) / 2
36 = x²
To find the value of x, we need to solve for it. Taking the square root of both sides of the equation:
√(36) = √(x²)
6 = x
Now that we have the length of leg YZ, which is x = 6 cm, we can find the length of leg XY:
XY = 2x = 2 * 6cm = 12cm
Therefore, the length of leg XY is 12 cm.
Let's assume the length of leg YZ is "x" cm. According to the problem, the length of leg XY is twice as long as leg YZ, so it would be 2x cm.
The formula for the area of a triangle is given by:
Area = (1/2) * base * height
In this case, the base would be the length of leg YZ (x cm) and the height would be the length of leg XY (2x cm).
Using the formula, we can calculate the area of the triangle:
36 cm^2 = (1/2) * x * 2x
To simplify further, we can multiply (1/2) * 2 to get:
36 cm^2 = x^2
Now, we can solve for x by taking the square root of both sides:
√(36 cm^2) = √(x^2)
6 cm = x
Therefore, the length of leg XY is twice the length of YZ, so it would be 2 * 6 cm = 12 cm.