Answered

Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

In the diagram below, EF || HG, EF = 5, HG = 12, FI = 1 4x + 3
and HI= 6.1x - 6.5.
What is the length of HI?

In The Diagram Below EF HG EF 5 HG 12 FI 1 4x 3 And HI 61x 65 What Is The Length Of HI class=

Sagot :

akposevictor

The length of HI in the similar triangles is: (4) 24.

What are Similar Triangles?

The corresponding sides of triangles that are similar to each other have ratios that are equal to each other, thus, they are proportional.

Triangle EFI and triangle GHI are similar to each other. Therefore, their corresponding sides have ratios that are equal. Thus, we will have the following:

HI/FI = HG/EF

Given:

EF = 5,

HG = 12,

FI = 1.4x + 3

HI = 6.1x - 6.5

Plug in the values

6.1x - 6.5/1.4x + 3 = 12/5

Cross multiply

5(6.1x - 6.5) = 12(1.4x + 3)

Open the bracket

30.5x - 32.5 = 16.8x + 36

30.5x - 16.8x = 32.5  + 36

13.7x = 68.5

Divide both sides by 13/7

13.7x/13.7 = 68.5/13.7

x = 5

HI = 6.1x - 6.5

Plug in the value of x

HI = 6.1(5) - 6.5

HI = 30.5 - 6.5

HI = 24

The length of HI in the similar triangles is: (4) 24.

Learn more about similar triangles on:

https://brainly.com/question/2644832

#SPJ1

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.