These polygons are similar find x. AB(14)BC(10) and A'B'(x+9)B'C'(x+6)

Answer 1

To find the value of \( x \) for the similar polygons ABBC and A'B'B'C', we can set up a proportion based on the corresponding sides of the polygons.

Given:

• \( AB = 14 \)
• \( BC = 10 \)
• \( A'B' = x + 9 \)
• \( B'C' = x + 6 \)

Since the polygons are similar, the ratio of the lengths of corresponding sides is equal. We can set up the following proportions:

1. For the sides \( AB \) and \( A'B' \): \[ \frac{AB}{A'B'} = \frac{BC}{B'C'} \]

Substituting the values, we get: \[ \frac{14}{x + 9} = \frac{10}{x + 6} \]

Now, we can cross-multiply to solve for \( x \): \[ 14(x + 6) = 10(x + 9) \]

Expanding both sides: \[ 14x + 84 = 10x + 90 \]

Now, isolate \( x \) by moving \( 10x \) to the left side and \( 84 \) to the right side: \[ 14x - 10x = 90 - 84 \] \[ 4x = 6 \]

Now, divide both sides by 4: \[ x = \frac{6}{4} = \frac{3}{2} = 1.5 \]

Thus, the value of \( x \) is \( \boxed{1.5} \).