HOW TO FIND THE VALUE OF UNKNOWN IN SIMILAR FIGURES

The two polygons are similar. Find the value of x.

Problem 1 :

Solution :

The two polygons are similar.

x = 43

Problem 2 :

Solution :

The two polygons are similar.

12/18 = 7/(x - 1)

Using cross multiplication.

12(x – 1)  = 18(7)

12x - 12 = 126

12x = 126 + 12

12x = 138

x = 11.5

Problem 3 :

Solution :

The two polygons are similar.

(4x + 3)/8 = 20/14

Using cross multiplication.

14(4x + 3) = 20(8)

56x + 42 = 160

Subtracting 42

56x = 160 - 42

56x = 118

x = 118/52

x = 2.27

Problem 4 :

Solution :

The two polygons are similar.

67^º = (5x – 3)^º

67 + 3 = 5x

70 = 5x

x = 14

Problem 5 :

Solution :

The two polygons are similar.

27/18 = 34.5/(5x - 7)

27(5x - 7) = 34.5(18)

135x - 189 = 621

135x = 621 + 189

135x = 810

x = 810/135

x = 6

Problem 6 :

Solution :

The two polygons are similar.

124^º = (3x + 4)^º

124 – 4 = 3x

120 = 3x

x = 120/3

x = 40

Problem 7 :

Solution :

The two polygons are similar.

36/30 = 15/(x + 5)

Using cross multiplication.

36(x + 5) = 30 × 15

36x + 180 = 450

Subtracting 180 on both sides.

36x = 450 – 180

36x = 270

x = 7.5

Problem 8 :

Solution :

The two polygons are similar.

(7x + 4)^º = 53^º

7x = 53 – 4

7x = 49^º

x = 49/7

x = 7

Problem 9 :

Solution :

The two polygons are similar.

61^º= (11x – 5)^º

61 + 5 = 11x

66 = 11x

66/11 = x

x = 6