Question

the side of triangle ABC and 5cm,8cm,and 7cm resprtivaly find out its semiperimetet​

Answer 1

s=a+b+c/2

=5+8+7/2

=10

Answer 2

$\underline\mathfrak\pink{Given:-}$

• The side of triangle ABC and 5cm, 8cm and 7cm.

$\large\underline\mathfrak{To \: find:-}$

• Find its semiperimeter ....?

$\large\underline\mathfrak\pink{Solutions:-}$

Area of ∆ABC

The sides of a triangle are:-

• A = 5cm
• B = 8cm
• C = 7cm

Area of triangle by heroe's formula:-

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

$\: \: \: \: \: \leadsto \: \: S \: \: = \: \: \frac{a \: + \: b \: + \: c}{2}$

• A = 5cm
• B = 8cm
• C = 7cm

$\: \: \: \: \: \leadsto \: \: S \: \: = \: \: \frac{{5} \: + \: {8} \: + \: {7}}{2}$

$\: \: \: \: \: \leadsto \: \: S \: \: = \: \: \frac{20}{2}$

$\: \: \: \: \: \leadsto \: \: S \: \: = \: \: {10}$

Semiperimeter is 10cm.

Area of triangular field:-

$\: \: \: \: \: \leadsto \: \: \sqrt{{10} \: ({10} \: - \: {5}) \: ({10} \: - \: {8}) \: ({10} \: - \: {7})}$

$\: \: \: \: \: \leadsto \: \: \sqrt{{10} \: \times \: {(5)} \: \times \: {(2)} \: \times \: {(3)}}$

$\: \: \: \: \: \leadsto \: \: \sqrt{300}$

$\: \: \: \: \: \leadsto \: \: {17.32} \: {cm}^{2}$

Hence, Area of triangle is 17.32 cm² and it's semiperimeter is 10cm.