Question

The side of a triangle are in a ratio 3:5:7 and it's perimeter is 300m . Find it's area.

Answer 1

Answer:

Step-by-step explanation:

Sides=3x,5x and 7x

Perimeter=300m

300=3x+5x+7x

300=15x

x=300/15

=20

Sides:-

3x=60m

5x=100m

7x=140m

semiperimeter,s=(a+b+c)/2

=60+100+140/2

=300/2

=150m

Area=√ [s(s-a)(s-b)(s-c)]

=√[150(150-60)(150-100)(150-140)

=√ 150×90×50×10

=√15×10×9×10×5×10×10

=10×10×3√5×3×5

=300×5√3

=1500√3 m2

Hope it helps you

Answer 2

Given:-

• The side of a triangle are in a ratio 3:5:7.
• it's perimeter is 300m .

To find:-

• Find it's area.

Solutions:-

• The area of a triangle having sides a, b, c.

By heroe's formula,

• A = √s(s - a)(s - b)(s - c)

where,

s = (a + b + c) / 2

• a = 3
• b = 5
• c = 7

perimeter = 300m

s = perimeter/2

s = 300/2

s = 150m

The side of the triangle.

a = 3x

b = 5x

c = 7x

since, 2s = 300

300 = 3x + 5x + 7x

300 = 15x

x = 300/15

x = 20

Now,

a = 3x

= 3 × 20

= 60

b = 5x

= 5 × 20

= 100m

c = 7x

= 7 × 20

= 140m

The area of the triangle = √s(s - a)(s - b)(s - c)

= √150(150 - 60)(150 - 100)(150 - 140)

= √150(90) (50) (10)

= 100√15 × 9 × 5

= 100√5 × 3 × 3 × 3 × 5

= 100 × 3 × 5√3

= 1500√3m²

hence, the area of the triangle is 1500√3m².