I need help with these:
Suppose triangleABC ~ triangleJKL with BC = 28, JK = 12, and KL = 42. Find the perimeter of triangleABC if the perimeter of triangleJKL is 72.
&
Find the scale factor of triangleDEF to triangleXYZ if triangleDEF ~ triangleXYZ, DE=10, XZ=20, and XY=45.
If I can help on these two, I can do the rest of my worksheet. Step by step would help a lot!
BC is to KL as perimeterABC is to 72
28/12=P/72
solve for P.
2)
De/XY= scale factor
10/45= scale factor
To solve the first problem, we are given that triangle ABC is similar to triangle JKL. Let's use the given information to find the perimeter of triangle ABC.
1) BC is to KL as the perimeter of ABC is to 72:
We are given that BC = 28, JK = 12, KL = 42, and the perimeter of JKL is 72.
We can set up the proportion:
BC / KL = perimeter of ABC / 72
Substituting the given values:
28 / 42 = perimeter of ABC / 72
Now, we solve for the perimeter of ABC:
Cross-multiplying gives:
28 * 72 = 42 * (perimeter of ABC)
Dividing both sides by 42 gives:
(28 * 72) / 42 = perimeter of ABC
Calculating the result gives:
48 = perimeter of ABC
So, the perimeter of triangle ABC is 48.
Now let's move on to the second problem:
2) To find the scale factor of triangle DEF to triangle XYZ, we are given DE = 10, XZ = 20, and XY = 45.
The scale factor is the ratio of corresponding side lengths between two similar triangles.
We can set up the following proportion:
DE / XY = scale factor
Substituting the given values:
10 / 45 = scale factor
Now, we can simplify the fraction:
2 / 9 = scale factor
Therefore, the scale factor of triangle DEF to triangle XYZ is 2/9.
I hope this explanation helps! Let me know if you have any further questions.