Two triangles are similar. The measure of the shortest side of the first triangle is 12 and the measure of the shortest side of the second triangle is 5. If the longest side of the first triangle measures 15, what is the measure of the longest side of the second triangle?
A.2.4
B. 6.25
C.24
D.36
6.25
6.25
correct
D.36
Well, let's do some math! Since the triangles are similar, we can set up a proportion to find the missing side.
The proportion would look like this:
(longest side of 1st triangle) / (shortest side of 1st triangle) = (longest side of 2nd triangle) / (shortest side of 2nd triangle)
15/12 = (longest side of 2nd triangle) / 5
Now, cross-multiply and solve for the longest side of the 2nd triangle:
15 * 5 = 12 * (longest side of 2nd triangle)
75 = 12 * (longest side of 2nd triangle)
(longest side of 2nd triangle) = 75/12
(longest side of 2nd triangle) = 6.25
So, the measure of the longest side of the second triangle is 6.25. Therefore, the answer is B. 6.25.
But hey, if you're feeling clowny, you can always pick C. 24 and see what happens! Who needs math when you have clown confusion?
To solve this problem, we can use the concept of similar triangles.
Similar triangles have their corresponding sides proportional. This means that if we have two similar triangles, we can set up a proportion to find the lengths of corresponding sides.
Let's set up a proportion using the shortest and longest sides of the two triangles:
(shortest side of first triangle) / (shortest side of second triangle) = (longest side of first triangle) / (longest side of second triangle)
Plugging in the given values, we have:
12 / 5 = 15 / x
To solve for x (the measure of the longest side of the second triangle), we can cross-multiply:
12 * x = 5 * 15
Now, we can solve for x by dividing both sides of the equation by 12:
x = (5 * 15) / 12
Calculating this, we get:
x ≈ 6.25
Therefore, the measure of the longest side of the second triangle is approximately 6.25. So the correct answer is option B.
Corresponding sides of similar triangles are in the same ratio.
So set up a proportion, let me know what you got.
D
5/12=15/X (cross multiply) ------> 5x=180 (divide both sides by 5) x=36