Finding missing measure of similar triangle .
1st triangle has
leg AB 3cm leg bc 9cm hypotenuse ac ?
2nd triangle has
Leg DE ? Hypotenuse EF 12cm and Leg DF is 10cm
What is AC?What is DE
in ABC, AC = √(3^2+9^2) = 3√10
DE = √(12^2-10^2) = 2√11
But the similarity is bogus, since 3/9 ≠ 22√11/10
You need to fix this up
To find the missing measure of similar triangles, we can use the concept of proportional reasoning.
Let's first find the missing measure in the 1st triangle:
1. Identify the corresponding sides of the similar triangles. In this case, we are comparing the sides of the first triangle (ABC) to the second triangle (DEF).
2. Write down the proportion based on the corresponding sides. Since the two triangles are similar, the ratios of corresponding sides will be equal. We can set up the proportion as follows:
(AB / DE) = (BC / EF) = (AC / DF)
Substitute the given values:
(3 / DE) = (9 / 12)
3. Solve the proportion for the missing measure. Cross-multiply and solve for DE:
3 * 12 = 9 * DE
36 = 9 * DE
DE = 36 / 9
DE = 4 cm
Therefore, the missing measure in the 2nd triangle is DE = 4 cm.
Now, let's find the missing measure in the 1st triangle:
1. Use the proportion we set up earlier:
(AB / DE) = (BC / EF) = (AC / DF)
2. Substitute the given values:
(AB / 3) = (BC / 12) = (AC / 10)
3. Solve the proportion for the missing measure. Cross-multiply and solve for AC:
AB * 10 = 3 * AC
3 * 10 = AB * AC
30 = AB * AC
Since we don't have the value of AB, we cannot determine the exact measure of AC.
Therefore, without knowing the value of AB, we cannot find the exact measure of AC in the 1st triangle.