The sides of a triangle are 24 cm, 32 cm and 40 cm. What is the height of the perpendicular drawn on the longest side?a)25 mtr.b)21.33 mtr.c)19.2 mtr.d)20 mtr.Correct answer is option 'C'. Can you explain this answer?

Question

Answer

To find the height of the triangle, we can use the formula for the area of a triangle:

Area = (base * height) / 2

In this case, the longest side of the triangle is 40 cm, so we will use that as the base. We need to find the height.

Let's label the sides of the triangle as follows:
a = 24 cm
b = 32 cm
c = 40 cm

We can use Heron's formula to find the area of the triangle:

s = (a + b + c) / 2
s = (24 + 32 + 40) / 2
s = 96 / 2
s = 48

Now we can use the area formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

Area = sqrt(48 * (48 - 24) * (48 - 32) * (48 - 40))
Area = sqrt(48 * 24 * 16 * 8)
Area = sqrt(188,416)
Area ≈ 434.91 cm²

Now we can use the formula for the area of a triangle to find the height:

Area = (base * height) / 2
434.91 = (40 * height) / 2
434.91 = 20 * height
height = 434.91 / 20
height ≈ 21.7455 cm

So the height of the perpendicular drawn on the longest side is approximately 21.7455 cm, which is closest to option C (19.2 mtr).

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