A triangle has sides of lengths 20, 28, and 32. A similiar triangle has a side of length 15 and another of length 24. How long is the third side of this triangle?
for similar triangles, the ratio of the sides of the first triangle is equal to the ration of the corresponding sides of the second triangle,, like:
let h1 = height of 1st triangle
let h2 = height of 2nd triangle
let b1 = base of 1st triangle
let b2 = base of 2nd triangle
therefore, if they are similar triangles,
(h1)/(b1) = (h2)/(b2)
thus in the question, we can write:
let x = third side
20/15 = 32/24 = 28/x
simplifying:
4/3 = 28/x
solving for the third side,
x = 21
hope this helps~ :)
20/15 = 4/3
28/24 = nope
32/24 = 4/3 yes
so
20 --> 15
32 --> 24
28(3/4) = 21
so
20 , 28 , 32
--->
15 , 21 , 24
To determine the length of the third side of the similar triangle, we can use the concept of ratios. Since the two triangles are similar, their corresponding sides are proportional.
First, we need to find the ratio between the corresponding sides of the two triangles. Let's choose the sides with the lengths 20 and 15. The ratio can be found by dividing the lengths of the corresponding sides:
Ratio = Length of Side in First Triangle / Length of Corresponding Side in Second Triangle = 20 / 15 = 4/3
Now, we can use this ratio to find the length of the third side of the similar triangle. Let's choose the side with the length 32 in the first triangle. We need to multiply this length by the ratio we found:
Length of Third Side = Length of Side in First Triangle * Ratio = 32 * (4/3) = 128/3 ≈ 42.67
Therefore, the length of the third side of the similar triangle is approximately 42.67 units.