# In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm. - Mathematics

MCQ
True or False

In a triangle, the sides are given as 11 cm, 12 cm and 13 cm. The length of the altitude is 10.25 cm corresponding to the side having length 12 cm.

• True

• False

#### Solution

This statement is True.

Explanation:

Since the sides of a triangle are a = 11 cm, b = 12 cm and c = 13 cm.

Now, semi-perimeter, s = (a + b + c)/2

= (11 + 12 + 13)/2 = 36/2 = 18 cm

Area of a triangle = sqrt(s(s - a)(s - b)(s - c))   ......[By Heron's formula]

= sqrt(18(18 - 11)(18 - 12)(18 - 13))

= sqrt(18 xx 7 xx 6 xx 5)

= sqrt(3 xx 6 xx 7 xx 6 xx 5)

= 6sqrt(3 xx 7 xx 5)

= 6sqrt(105)

= 6 xx 10.25

= 61.5 cm2

∴ Area of ΔABC = 1/2 xx BC xx AD  ......[because "Area of triangle" = 1/2 ("base" xx "height")]

= 1/2 xx 12 xx 1025

= 6 xx 10.25

= 61.5 cm2

Is there an error in this question or solution?
Chapter 12: Heron's Formula - Exercise 12.2 [Page 115]

#### APPEARS IN

NCERT Exemplar Mathematics Class 9
Chapter 12 Heron's Formula
Exercise 12.2 | Q 9 | Page 115

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