Question

Find the value of x that makes AFGH~AJKL.
(Lesson 11.3) (1 point)
X+3.5
20

Answer 1

Answer: The answer is: " x = 2.833333333333...." .

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or: write as: " 2
`(5)/(6)` " .

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Explanation:

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Set up a ratio:

Note: Segment FH = (x + 35)

Segment JL = 20 ;

Segment FH ~ Segment JL ;

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Note: Segment GH = (x - 4) ;

Segment KL = 5 ;

Segment GH ~ Segment KL .

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So, ( x + 3.5) : 20 :: (x-4) : 5 ;

Write this ratio in fraction format:

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→
`((x+3.5) )/(20 ) = ((x-4) )/(5)` ;

Now; "cross-factor multiply" :

→
`(a)/(b) = (c)/(d )` ; →
`ad = bc` ; {
`{ a\\eq0 ; b\\eq0 ; c\\eq0 ; d\\eq0` .}.

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So:

5(x + 3.5) = 20(x - 4) ;

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→ To simplify, start by divide each side of the equation by "5" ;

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→ {5(x + 3.5) } / 5 = { 20(x - 4) } / 5 ;

to get:

→ (x + 3.5) = 4(x - 4) ;

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Now, on the right-hand side of the equation;

let us expand the expression;

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We have the expression: " 4(x - 4) " ;

To expand:

Note the "distributive property of multiplication:

→ a(b + c) = ab + ac ;

Likewise:

→ 4(x - 4) = 4x - 16 ;

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Now, we can rewrite our equation:

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→ " x + 3.5 = 4x - 15 " ;

Now, we can subtract "x" from each side of the question;

& add "15" to each side of the equation; as folllows:

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→ x + 3.5 = 4x - 15 ;

- x + 15 = - x +15

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to get: 8.5 = 3x ;

↔ 3x = 8.5 ;

Now, divide each side of the equation by "3" ;

to isolate "x" on one side of the equation;

& to solve for "x" ; as follows:

→ 3x / 3 = 8.5 / 3 ;

to get: x = 8.5 /3

= 2.83333333333 ;

or; write as: " 2
`(5)/(6)` ."

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Hope this is helpful to you! Best wishes!

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