Question

find the area of the triangle whose side are 10cm,24cm and 26cm.

Answer 1

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Here we have :-

a = 10 cm

b = 24 cm

c = 26 cm

★We have to Find Side,

★Using Formula we get :-

$\tt{\rightarrow s=\dfrac{10+24+26}{2}}$

$\tt{\rightarrow s=\dfrac{60}{2}}$

= 30

$\large{\fbox{Using\;Herons\;Formula}}$

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

$\tt{\rightarrow\sqrt{30(30-10)(30-24)(30-26)}}$

$\tt{\rightarrow\sqrt{30\times 20\times 6\times 4}}$

$\tt{\rightarrow\sqrt{2\times 3\times 5\times 2\times 2\times 5\times 3\times 2\times 2\times 2}}$

= 2 × 2 × 2 × 3 × 5

= 120 cm²

Answer 2

Question :-

Find the area of the triangle whose side are 10cm, 24cm, and 26cm.

Solution :-

Given that the three sides of a triangle are 10cm, 24cm and 26cm.

> a = 10cm

> b = 24cm

> c = 26cm

As the semi-perimeter is the half of the sum of sides of triangle.

$s \: = \: \frac{a + b + c}{2} \\ s \: = \: \frac{10 + 24 + 26}{2} \\ s \: = \frac{60}{2} \\ s \: = \: 30$

Therefore area of triangle =

$= \: \sqrt{s \: (s - a) \: (s - b) \: (s - c)} \\ = \sqrt{30 \: (30 - 10) \: (30 - 24) \: (30 - 26)} \\ = \sqrt{30 \times 20 \times 6 \times 4} \\ = \sqrt{2 \times 3 \times5 \times 2 \times 2 \times 5 \times 3 \times 2 \times 2 \times 2} \\ =2 \times 2 \times 2 \times 3 \times 5 \\ = 120 {cm}^{2}$