Question

metre of a triangle 2 is to 3 is to 5 and its perimeter 120 find the area of a triangle ​

Answer 1

$\bf\huge\underline\red{ANSWER}$

Given:

Measure of a triangle = 2:3:5

So, let x be the common multiple of this ratio, then,

2 × x = 2x = a

3 × x = 3x = b &

5 × x = 5x = c

Perimeter of the triangle = 120 units.

•°• Perimeter of the $\text{triangle}$ = 2x + 3x + 5x $\bf\underbrace {Perimeter = sum\: of\:all\: sides}$

120 = 10x

x = $\bf\large\frac{120}{10}$

x = 10 units.

Side a = 2x = 2× 10 = 20 units.

Side b = 3x = 3 × 10 = 30 units.

Side c = 5x = 5 × 10 = 50 units.

Now we will use Heron's formula to calculate the area of the triangle,

So,

Perimeter = ½ × 120

Perimeter = s = 60.

By Heron's formula,

√s(s-a)(s-b)(s-c)

√60(60-20)(60-30)(60-50)

√60 × 40 × 30 × 10

√720000

Area of the triangle = 848.4 sq. units