Question

1. Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200

​

Answer 1

CORRECT QUESTION :

• Find the area of a triangle whose sides are 150 cm, 120 cm and 200 cm respectively.

GIVEN :

• The sides of a triangle are 150 cm, 120 cm, 200 cm.

TO FIND :

• The area of a triangle = ?

FORMULA USED :

• Heron's formula :- $\sf \sqrt {s(s-a)(s-b)(s-c)}$

SOLUTION :

To find the area of a triangle,

By using heron's formula,

Area of a triangle :- $\sf \sqrt {s(s-a)(s-b)(s-c)}$

$\sf S \ = \ \dfrac {150+120+200}{2}$

$\sf S \ = \ 235 \ cm$

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

$\implies \sf \sqrt {235 (235-150)(235-120)(235-200)}$

$\implies \sf \sqrt {235 \times 85 \times 115 \times 35}$

$\implies \sf \sqrt {80399375}$

$\implies \sf Area \ = \ 8966.57 \ cm^{2}$

$\therefore$ The area of a triangle is 8966.57 cm².

Answer 2

$a=200cm, b=150cm, c=120cm</p><p> \\ s = \frac{a + b + c}{2} = \frac{200 + 150 + 120}{2} = \frac{470}{2} = 235cm \\ </p><p>Area \: of \: triangle \\ = \sqrt{s(s - a)(s - b)(s -c )} \\ = \sqrt{235(235 - 200)(200 - 150)(235 - 120)} \\ = \sqrt{235 \times 35 \times 50 \times 115} \\ = \sqrt{47293750} \\ = 25\sqrt{75670} \\ = 6877.04 {cm}^{2}$