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Question
The measurements of ΔLMN and ΔABC are shown in the figure given below. The length of side AC is ______.
Options
16 cm
7 cm
8 cm
4 cm
MCQ
Fill in the Blanks
Solution
The measurements of ΔLMN and ΔABC are shown in the figure given below. The length of side AC is 8 cm.
Explanation:
∠M = ∠B = 130°
∠N = ∠C = 28°
∴ By AA similarity
ΔLMN ∼ ΔABC
∴ `"LM"/"AB" = "MN"/"BC" = "LN"/"AC"`
`45/5 = 63/"BC" = 72/"AC"`
`45/5 = 72/"AC"`
45 × AC = 5 × 72
`AC = (5 xx 75)/45`
∴ AC = 8 cm
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