Question

find the area of ∆ if the sides are A=30cm ; B=40 cm and C=50 cm​

Answer 1

Answer:

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 ,

\begin{gathered} \sqrt{s \: ( \:s \: - \: a)(s \: - b)(s \: - c) } \\ \end{gathered}

s(s−a)(s−b)(s−c)

Put the required 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}

60(60−30)(60−40)(60−50)

60×30×20×10

2×5×3×2×2×5×3×2×5×2×2×5

2×2×2×3×5×5

600cm

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