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In the given 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 given 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,

MO^{2} = MN^{2} + NO^{2}

= 6^{2} + 8^{2}

= 36 + 64

⇒ MO^{2} = 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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