Question

Find length of GF in the given figure?

Answer 1

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 $ = 7units $
Length of GF $ = 3x\,units $
Length 0f HF $ = \left( {9x + 1} \right)\,units $
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 $ HF = HG + GF $ from the figure given to us.
Hence, $ \left( {9x + 1} \right)\, = 7 + 3x $
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, $ \left( {9x + 1} \right)\, = 7 + 3x $
 $ \Rightarrow 9x - 3x = 7 - 1 $
Simplifying further, we get,
 $ \Rightarrow 6x = 6 $
 $ \Rightarrow x = 1 $
Hence, we got the value of x as $ 1\,unit $ .
So, the length of line segment GF $ = 3x = 3\,units $
Hence, Length of GF is $ 3\,units $ .
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.