Triangle HDK is similar to triangle LMN. Which proportion can be used to calculate the length of LM (line above LM) in centimeters?
( There are two triangles the one on the left has H at the top then it slopes down and in the middle is 7.5 cm. Then a K at the bottom tip. On the left of that triangle as H slopes down on the left it has 4.5 cm then on the bottom of that triangle it has 6 cm. That is the dimensions of #1. #2 Triangle is on the right side. It has an L at the very top of the tip then it slopes down on the right and has 11.35 cm. Then as it goes to the. bottom on the right side it has N. On the left side it slopes from the tip of L to the bottom and it has an M. Then across the bottom it has 9 cm. That is theTriangle #2 on the right side.
The answers are;
A. 7.5/11.25 = LM/4.5
B. 6/7.5 = LM/9
C. 11.25/LM= 4.5/7.5.
D. 9/LM = 6/4.5.
My answer I think is D but I don’t know how to figure it out! Can someone help please to give step by step on how to come out to answer D? I would deeply appreciate it!!!
To determine the correct proportion to calculate the length of LM (line above LM) in centimeters, we need to find the corresponding sides of the similar triangles HDK and LMN.
Let's compare the given sides of the two triangles:
Triangle HDK:
- Side HK = 7.5 cm
- Side HD = 4.5 cm
- Side DK = 6 cm
Triangle LMN:
- Side LN = 11.35 cm
- Side LM (the one we want to find) = ?
- Side MN = 9 cm
To find the corresponding sides between the two triangles, HDK and LMN, we can set up the proportion:
(Length of corresponding side in HDK) / (Length of corresponding side in LMN) = (Length of another side in HDK) / (Length of another side in LMN)
Now let's compare the sides:
HD (in HDK) corresponds to LM (in LMN)
4.5 / LM = ?
6 (in HDK) corresponds to 9 (in LMN)
6 / 9 = ?
To find the length of LM, we can cross-multiply and solve for LM:
4.5 * 9 = 6 * LM
40.5 = 6 * LM
Divide both sides by 6 to isolate LM:
40.5 / 6 = LM
LM = 6.75 cm
Therefore, the correct proportion to calculate the length of LM in centimeters is:
D. 9 / LM = 6 / 4.5