Question

The three sides of a triangle is 30cm, 40cm and 50cm, find the height of the triangle corresponding to longest side.​

Answer 1

Given :-

Here , Three sides of triangle are given 30cm , 40cm and 50 cm

Solution :-

Let the sides of the triangle be a , b and c

Here , a = 30cm , b = 40cm and c = 50cm

Therefore ,

S = a + b + c /2

S = 30 + 40 + 50 / 2

S = 120/2

S = 60

Now , By using Heron's Formula ,

$\sqrt{s \: ( \:s \: - \: a)(s \: - b)(s \: - c) }$

Put the required values ,

$\sqrt{60 ( 60 - 30) \: ( 60 - 40)( 60 - 50)} \\ \sqrt{60 \times 30 \times 20 \times 10 } \\ \sqrt{2 \times 5 \times 3 \times 2\times 2 \times 5 \times 3 \times 2 \times 5 \times 2 \times 2 \times 5 } \\ 2 \times 2 \times 2 \times 3 \times 5 \times 5 \\ 600 {cm}^{2}$

Here , Area of triangle

= 1/2 * base * height

600 = 1/2 * 50 * h

600 * 2 = 50 * h

1200 /50 = h

h = 24cm

Hence , The height of triangle corresponding to longest side = 24cm

Answer 2

Answer:

$\huge\fbox{Diagram}$

• Diagram has been created by me , see in the above attachment

$\huge\fbox{Concept}$

• As given the sides (30 ,40 ,50 )cm. We have to find the height. So first of all we will used the formula
• $\large \rm \bold \red {s = \frac{a + b + c}{2} }$to find the (s) .Then we will used the heron's formula $\large \bf \red{ area \: of \: the \: traingle = \sqrt{s(s} - a)(s - b)(s - c)}$ then we will used the formula 1/2× base× height . By this we will get the height.

$\huge\fbox{Given}$

As you can understand it is an scalene traingle so

• a = 30 cm
• b = 40 cm
• c = 50 cm

$\huge\fbox{To \:find}$

• The height

$\huge\fbox{Solution}$

Let ,

• a = 30 cm
• b = 40 cm
• c = 50 cm

$\therefore \bf s = \frac{a + b + c}{2} \\ \\ \bf s = \frac{30 + 40 + 50}{2} \\ \\ \bf s = \cancel\frac{120}{2} \\ \ \\ \bf \: s = 60 \: cm$

Now ,

• s - a = 60 - 30 = 30
• s - b = 60 - 40 = 20
• s - c = 60 - 50 = 10

you can put the values directly instead of putting 60- 30 but I will give by long method .

$\large \bf \red{ area \: of \: the \: traingle = \sqrt{s(s} - a)(s - b)(s - c)}$

Put the values:-

$\begin{gathered} \sqrt{60 ( 60 - 30) \: ( 60 - 40)( 60 - 50)} \\ \sqrt{60 \times 30 \times 20 \times 10 } \\ \sqrt{2 \times 5 \times 3 \times 2\times 2 \times 5 \times 3 \times 2 \times 5 \times 2 \times 2 \times 5 } \\ 2 \times 2 \times 2 \times 3 \times 5 \times 5 \\ 600 {cm}^{2} \end{gathered}$

Here , Area of triangle

= 1/2 × base × height

600 = 1/2 × 50 × h

600 × 2 = 50 h

1200 /50 = h

h = 24cm