FINDING MISSING SIDES OF SIMILAR FIGURES WORKSHEET

Use the diagram shown below to answer the problems given below. 

Problem 1 : 

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

k = 9, n = 6, o = 8, p = 4

Problem 2 : 

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

k = 24, l = 30, m = 15, n = 16

Problem 3 :

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

m = 11, p = 6, n = 5, o = 4

Problem 4 : 

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

k = 16, l = 13, m = 12, o = 7

Detailed Answer Key

Problem 1 : 

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

k  =  9, n  =  6, o  =  8, p  =  4

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

KL/NO  =  LM/OP   =  KM/NP

m/p  =  k/n  =  l/o

k  =  9, n  =  6, o  =  8, p  =  4

m/4  =  9/6  =  l/8

So, the missing sides of the triangle KLM are 6 and 12.

Problem 2 : 

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

k  =  24, l  =  30, m  =  15, n  =  16

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

KL/NO  =  LM/OP   =  KM/NP

m/p  =  k/n  =  l/o

k  =  24, l  =  30, m  =  15, n  =  16

15/p  =  24/16  =  30/o

So, the missing sides of the triangle KLM are 10 and 20.

Problem 3 :

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

m  =  11, p  =  6, n  =  5, o  =  4

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

KL/NO  =  LM/OP   =  KM/NP

m/p  =  k/n  =  l/o

m  =  11, p  =  6, n  =  5, o  =  4

11/6  =  k/5  =  l/4

So, the missing sides of the triangle KLM are 9.16 and 7.33.

Problem 4 : 

Find the measures of the missing sides if  ΔKLM ∼ ΔNOP.

k  =  16, l  =  13, m  =  12, o  =  7

Solution :

Because the above triangles ΔKLM are ΔNOP similar, the lengths of corresponding sides are proportional.

Then,

KL/NO  =  LM/OP   =  KM/NP

m/p  =  k/n  =  l/o

k  =  16, l  =  13, m  =  12, o  =  7

12/p  =  16/n  =  13/7

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