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
m/4 = 9/6 m = 9(4) / 6 m = 36/6 m = 6 | l/8 = 9/6 l = 9(8) / 6 l = 72/6 l = 12 |
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
15/p = 24/16 p = 15(16) / 24 p = 240/24 p = 10 | 30/o = 24/16 o = 30(16) / 24 o = 480/24 o = 20 |
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
11/6 = k/5 k = 11(5) / 6 k = 55/6 k = 9.16 | l/4 = 11/6 l = 11(4) / 6 l = 44/6 l = 7.33 |
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
12/p = 13/7 p = 12(7) / 13 p = 84/13 p = 6.46 | 16/n = 13/7 n = 16(7) / 13 l = 44/6 l = 8.61 |
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