On the left triangle, the shorter side is labeled 4 inches and the longer side is labeled 10 inches. On the right triangle, the shorter side is labeled x inches and the longer side is labeled 20 inches.
The two triangles above are similar. Find the value of x. Be sure to explain your steps.
4/X = 10/20.
To find the value of x, we can use the property of similar triangles, which states that corresponding sides of similar triangles are proportional.
Given that the shorter side of the left triangle is 4 inches and the longer side is 10 inches, we can set up the following ratio between the shorter and longer sides:
4/10 = x/20
To solve for x, we can cross multiply:
10x = 4 * 20
10x = 80
Now, divide both sides of the equation by 10 to isolate x:
x = 80/10
x = 8
Therefore, the value of x is 8 inches.
To solve this problem, we can first set up a proportion between the side lengths of the two similar triangles. Proportions allow us to compare corresponding sides of similar shapes.
The proportion we can set up for the sides is:
4 / 10 = x / 20
To solve for x, we can cross-multiply and then solve for x.
First, we cross-multiply:
4 * 20 = 10 * x
Simplifying this expression gives us:
80 = 10x
To isolate x, we divide both sides of the equation by 10:
x = 80 / 10
Simplifying further, we find that x is equal to:
x = 8
Therefore, the value of x is 8 inches.