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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.

#### Options

True

False

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#### 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 cm^{2}

∴ 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 cm^{2}

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