
Find length of GF in the given figure?

Answer
464.4k+ views
Hint: The given question requires us to find the length of a line segment. In the problem given to us, we have to first convert the geometrical problem into an algebraic equation and then solve it with the help of algebraic rules and methods like the transposition rule so as to find the value of variable x in the equation. Then, we put in the value of variable x in the expression of length of the sides to find the length of GF that is asked in the question.
Complete step by step solution:
Length of HG
Length of GF
Length 0f HF
As the lengths of the sides are given to us as algebraic expressions. Hence, we need to convert the problem into an algebraic equation that we can solve easily.
So, we know that from the figure given to us.
Hence,
So, we have turned the given problem into an algebraic equation. Now, we just have to solve the equation obtained with help of algebraic rules and methods like the transposition rule so as to find the value of variable x in the equation.
So,
Simplifying further, we get,
Hence, we got the value of x as .
So, the length of line segment GF
Hence, Length of GF is .
So, the correct answer is “3 units”.
Note: Transposition rule involves doing the same mathematical thing or operation on both sides of an algebraic equation as this does not alter the equation and the equation remains unchanged. We have used it here and found the result as lengths of both lines segment are the same.
Complete step by step solution:

Length of HG
Length of GF
Length 0f HF
As the lengths of the sides are given to us as algebraic expressions. Hence, we need to convert the problem into an algebraic equation that we can solve easily.
So, we know that
Hence,
So, we have turned the given problem into an algebraic equation. Now, we just have to solve the equation obtained with help of algebraic rules and methods like the transposition rule so as to find the value of variable x in the equation.
So,
Simplifying further, we get,
Hence, we got the value of x as
So, the length of line segment GF
Hence, Length of GF is
So, the correct answer is “3 units”.
Note: Transposition rule involves doing the same mathematical thing or operation on both sides of an algebraic equation as this does not alter the equation and the equation remains unchanged. We have used it here and found the result as lengths of both lines segment are the same.
Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹37,300 per year
Recently Updated Pages
Master Class 8 Science: Engaging Questions & Answers for Success

Master Class 8 English: Engaging Questions & Answers for Success

Master Class 8 Social Science: Engaging Questions & Answers for Success

Master Class 8 Maths: Engaging Questions & Answers for Success

Class 8 Question and Answer - Your Ultimate Solutions Guide

Master Class 11 Economics: Engaging Questions & Answers for Success

Trending doubts
Write five sentences about Earth class 8 biology CBSE

Name the states through which the Tropic of Cancer class 8 social science CBSE

List some examples of Rabi and Kharif crops class 8 biology CBSE

In a school there are two sections of class X section class 8 maths CBSE

Explain land use pattern in India and why has the land class 8 social science CBSE

State the differences between manure and fertilize class 8 biology CBSE
