ABC is triangle in which AB = 3 cm, BC= 5 cm and AC = 4 cm. AD is a perpendicular from A to BC. Find the length of AD.

Created: 4 weeks ago | Updated: 3 weeks ago

Job Solution Premier Bank Ltd Premier Bank Ltd. || Junior Officer (2019) || 2019 গণিত

Here, three arms of the triangle are a = BC = 5cm ; b = AC = 4cm c = AB = 3cm

So perimeter of the triangle is a + b + c = (5 + 4 + 3) = 12cm

$∴$ Half of the perimeter, s = $\frac{12}{2}$ = 6

$∴$ Area of the triangle is = $\sqrt{s (s - a) (s - b) (s - c)}$ = $\sqrt{6 (6 - 5) (6 - 4) (6 - 3)}$ = $\sqrt{6 \times 1 \times 2 \times 3}$ = $\sqrt{36}$ = $\sqrt{6^{2}}$ = 6

And again, Area of the triangle is = $\frac{1}{2}$ $\times$ base $\times$ height= $\frac{1}{2}$ × 5 × AD

As of question, $\frac{1}{2}$ $\times$ 5 $\times$ AD = 6

=AD = $\frac{6 \times 2}{5} = \frac{12}{5} = 2.4 c . m .$

Answer: 2.4 cm.

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