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 ______. - Mathematics

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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,

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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Chapter 9: Perimeter and Area - Exercise [Page 272]

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NCERT Exemplar Mathematics Class 7
Chapter 9 Perimeter and Area
Exercise | Q 17. | Page 272

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