Question

Find the area of triangle two sides of which are 80 cm and 50 cm and the perimeter is 250 cm.

Answer 1

Answer:

perimeter of triangle = sum of all sides of the triangle,

let the third side be x

250cm = 80cm + 50cm + x cm

250 cm = 130cm + x cm

x = 250cm - 130cm

x = 120cm

Hence sides of triangle = 80cm, 50cm, 120cm

According to Heron's formula

Area of triangle =

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

where,

$s = \frac{a + b + c}{2}$

and a,b,c are the sides of the triangle,

Hence, a = 80cm, b= 50cm, c = 120 cm

Therfore,

$\\ s = \frac{80 + 50 + 120}{2} \\ s = \frac{250}{2} \\ s = 125$

Area,

$= \sqrt{125(125 - 80)(125 - 50)(125 - 120)} \\ = \sqrt{125 \times 45 \times 75 \times 5} \\ = \sqrt{2109375} \\ = 1452.36 \: cm {}^{2}$

Step-by-step explanation:

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