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
∴ [tex]\frac{AB}{LM}[/tex] = [tex]\frac{BC}{MN}[/tex]
∵ AB = 14 and LM = x + 9
∵ BC = 10 and MN = x + 6
→ Substitute them in the ratio up
∴ [tex]\frac{14}{x+9}[/tex] = [tex]\frac{10}{x+6}[/tex]
→ 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
