Question

Each pair of polygons is similar. Find the value of x.

Answer 1

Answer:

The value of x is 1.5

Step-by-step explanation:

In similar figures, corresponding sides have the same ratio

In the given figure

∵ There are 2 similar polygons

∴ We must write their names with corresponding angles

∵ ∠A = ∠L, ∠B = ∠M, ∠C = ∠N, ∠D = ∠P

∴ Their names are ABCD and LMNP

→ By using the rule above

∴ Their corresponding sides have the same ratio

∴ $\frac{AB}{LM}$ = $\frac{BC}{MN}$

∵ AB = 14 and LM = x + 9

∵ BC = 10 and MN = x + 6

→ Substitute them in the ratio up

∴ $\frac{14}{x+9}$ = $\frac{10}{x+6}$

→ By using the cross multiplication

∵ 14 × (x + 6) = 10 × (x + 9)

∴ 14(x) + 14(6) = 10(x) + 10(9)

∴ 14x + 84 = 10x + 90

→ Subtract 10x from both sides

∵ 14x - 10x + 84 = 10x - 10x + 90

∴ 4x + 84 = 90

→ Subtract both sides by 84

∵ 4x + 84 - 84 = 90 - 84

∴ 4x = 6

→ Divide both sides by 4 to find x

∴ x = 1.5

∴ The value of x is 1.5