Question

The length of the sides of a triangle are 9 CM 12 cm and 15 cm find the length
of the altitude corresponding to the shortest side

Answer 1

Answer:

The length of altitude corresponding to shortest side is 12 meters .

Step-by-step explanation:

Given as :

For Any Triangle ABC

The length of side AB = 12 cm

The length of side BC = 9 cm

The length of side AC = 15 cm

Let The length of altitude corresponding to shortest side = h meter

Applying Heron's formula

S = $\dfrac{a+b+c}{2}$

Or, S = $\dfrac{12+9+15}{2}$

Or, S =$\dfrac{36}{2}$ = 18

Area of triangle = $\sqrt{S(S - a) (s-b) (s-c)}$

Or, Area of triangle = $\sqrt{18 (18 - 12) ( 18 - 9 ) ( 18 - 15 )}$

Or, Area of triangle = $\sqrt{18\times 6\times 3\times 9}$

Or,  Area of triangle = $\sqrt{2916}$

∴   Area of triangle = 54  m²

So, The Area of triangle =  54 m²

Now, Corresponding to shortest side , i.e BC = 9 cm

∵ Area of triangle =  $\dfrac{1}{2}$ × height × base

Or, 54 m² = $\dfrac{1}{2}$ × h × BC

Or, 54 × 2 = h × 9

∴     h = $\dfrac{108}{9}$

i.e  h = 12 m

So, The length of altitude corresponding to shortest side = h = 12 meter

Hence, The length of altitude corresponding to shortest side is 12 meter . Answer

Answer 2

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