Triangles Rst and wxy are similar .
the side lengths of rst are 10 inches. 14 inches and 20 inches and the length of an altitude is 6.5 inches. The shortest side of wxy.
Find the lengths of the other two sides of wxy.
Find the length of the corresponding altitude of wxy.
Shortest side of wxy missing.
kmlkm
To find the lengths of the other two sides of triangle WXY, as well as the length of its corresponding altitude, we can use the concept of similarity between triangles.
When two triangles are similar, it means that their corresponding sides are proportional. In this case, triangles RST and WXY are similar.
Given that the side lengths of triangle RST are 10 inches, 14 inches, and 20 inches, and the length of the altitude is 6.5 inches, we can setup the following proportion:
(Length of corresponding side in WXY) / (Length of corresponding side in RST) = (Length of altitude in WXY) / (Length of altitude in RST)
Let's denote the length of the shortest side in WXY as 'a'.
Using the proportion, we have:
(a) / (10) = (Length of altitude in WXY) / (6.5)
To find 'a', let's solve for it.
(a) / (10) = (Length of altitude in WXY) / (6.5)
Cross-multiplying, we get:
(a) * (6.5) = (10) * (Length of altitude in WXY)
Simplifying further:
6.5a = 10*(Length of altitude in WXY)
Finally, divide both sides by 6.5:
a = (10 * Length of altitude in WXY) / 6.5
To find the lengths of the other two sides of WXY, you can multiply each side length of RST by the same ratio, since the triangles are similar. Let's call the second longest side of WXY as 'b', and the longest side as 'c'.
b = (14 * Length of altitude in WXY) / 6.5
c = (20 * Length of altitude in WXY) / 6.5
In summary, to find the lengths of the other two sides of WXY, as well as the length of the corresponding altitude, you can use the formulas mentioned above.
Note: Please substitute the value of the "Length of altitude in WXY" in the formulas with the given length of the altitude.