Question

if the sides of a triangle are 150cm, 120cm, 200cm. find its area​

Answer 1

Answer:

Area = 8966.56cm²

Explanation:

Given three sides of the triangle are 150cm, 120cm, and 200cm.

Using Heron's formula :

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

Where,

• a, b, and c denotes the three sides of the triangle 120cm, 150cm, and 200cm respectively.
• s is the semi-perimeter.

Calculating s :-

$\rm \longrightarrow \: s = \dfrac{a + b + c}{2}$

$\rm \longrightarrow \: s = \dfrac{120 + 150 + 200}{2}$

$\rm \longrightarrow \: s = \dfrac{470}{2}$

$\rm \longrightarrow \: s = 235cm$

Substituting the values in the formula :-

$\rm \longrightarrow \: \sqrt{235(235 - 120)(235 - 150)(235 - 200)}$

$\rm \longrightarrow \: \sqrt{235(115)(85)(35)}$

$\rm \longrightarrow \: \sqrt{8093375}$

$\rm \longrightarrow \: 8966.56 {cm}^{2}$

∴ Area of the traingle is 8966.56cm²