The side lengths of △HIJ are 14, 28, and 35 units. The length of the longest side of △KLM is 40 units. If △HIJ and △KLM are similar, what is the length of the second longest side of △KLM?
Question
The side lengths of △HIJ are 14, 28, and 35 units. The length of the longest side of △KLM is 40 units. If △HIJ and △KLM are similar, what is the length of the second longest side of △KLM?
Solution
To solve this problem, we need to understand that similar triangles have proportional sides.
Step 1: Identify the longest side in △HIJ. This is 35 units.
Step 2: Identify the ratio between the longest side of △KLM and △HIJ. This is 40/35 = 8/7.
Step 3: Identify the second longest side in △HIJ. This is 28 units.
Step 4: Multiply the second longest side in △HIJ by the ratio we found in step 2 to find the length of the second longest side in △KLM. This is 28 * (8/7) = 32 units.
So, the length of the second longest side of △KLM is 32 units.
Similar Questions
List the side lengths of △GHI in order from smallest to largest, given that m∠G=14s+17°, m∠H=70s–37°, and m∠I=89s+27°.
List the side lengths of △CDE in order from smallest to largest, given that m∠C=96°, m∠D=44°, and m∠E=40°.
Context:△ABC and △DEF are similar. Find the missing side length.ABCDEF3663455?7(The triangles are not drawn to scale.) Answer question
One of the angles of △LMN has a measurement of 56°. One of the angles of △PQR has a measurement of 32°. If △LMN and △PQR are similar, what is the measurement of the largest angle of △LMN?
Triangle XYZ𝑋𝑌𝑍 is similar to triangle RST𝑅𝑆𝑇 such that X𝑋, Y𝑌, and Z𝑍 correspond to R𝑅, S𝑆, and T𝑇, respectively. The measure of ∠S∠𝑆 is 39°39° and 2XZ=RT2𝑋𝑍=𝑅𝑇. What is the measure of ∠Y∠𝑌?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.