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How do i solve for x?

How do i solve for x?-example-1

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The numerical value of x in the expression for the side lengths of the triangle is 3.

The figure in the image depicts two similar triangles.

From the figure:

Side 1 of the smaller triangle = x + 3

Side 2 of the smaller triangle = 2

Side 1 of the larger triangle = x + 18

Side 2 of the larger triangle = x + 4

To solve for the value of x, we use proportion since the two triangles are similar:

(x + 3)/2 = (x + 18)/(x + 4)

Cross multiply:

2( x + 18 ) = ( x + 3 )( x + 4 )

2x + 36 = x( x + 4 ) + 3( x + 4 )

2x + 36 = x² + 4x + 3x + 12

2x + 36 = x² + 7x + 12

x² + 7x - 2x + 12 - 36 = 0

x² + 5x - 24 = 0

Next, factor using AC method:

( x - 3 )( x + 8 ) = 0

Equate each factor to 0 and solve for x:

( x - 3 ) = 0

x - 3 = 0

x = 2

( x + 8 ) = 0

x + 8 = 0

x = -8

Since we are dealing with dimensions, we take the positive value.

Hence, the value of x is 3.

User Matt Robinson
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