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Question
In the following figure, ΔMNO is a right-angled triangle. Its legs are 6 cm and 8 cm long. Length of perpendicular NP on the side MO is ______.
Options
4.8 cm
3.6 cm
2.4 cm
1.2 cm
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Solution
In the following figure, ΔMNO is a right-angled triangle. Its legs are 6 cm and 8 cm long. Length of perpendicular NP on the side MO is 4.8 cm.
Explanation:
Given, ΔMNO is a right angled triangle.
So, according to Pythagoras theorem,
MO2 = MN2 + NO2
= 62 + 82
= 36 + 64
⇒ MO2 = 100
⇒ MO = `sqrt(100)`
⇒ MO = 10 cm
∴ Area of ΔMNO = `1/2` × Base × Height
⇒ `1/2` × MN × NO = `1/2` × MO × NP
⇒ `1/2` × 6 × 8 = `1/2` × 10 × NP
⇒ NP = `24/5`
⇒ NP = 4.8 cm
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