Question

The sides of a triangle are in the ratio 5:7:8 and its perimeter is 300 cm. Find its area.​

Answer 1

Step-by-step explanation:

let the sides be 5x, 7x, 8x

Perimeter of triangle = Sum of all sides of triangle

300 = 5x + 7x + 8x

300 = 20x

300/20 = x

x = 15 ✔️✔️

Therefore the 3 sides are :

5x = 5×15 = 75cm

7x = 7×15 = 105cm

8x = 8×15 = 120cm

3 sides of triangle are given. So, we will use heron's formula to find the area

_____________

Area of triangle = √ s (s-a) (s-b) (s-c)

where a, b, c are sides and s = semi perimeter

s = p/2 = 300/2 = 150

_______________

Area of triangle = √150(150-75)(150-105)(150-120)

______________

= √150 × 75 × 45 × 30

________

= √15,187,500

= 3897.11431703 cm²

Answer 2

Step-by-step explanation:

Ratio of Sides of a triangle → 5:7:8

Perimeter of triangle → 300 cm

Let the sides of Traingle be 5x , 7x & 8x

We know that

Perimeter of ∆ = Sum of its sides

300 = 5x + 7x + 8x

20x = 300

x = 15

Sides of Triangle

• 5x = 5×15 = 75 cm
• 7x = 7×15 = 105 cm
• 8x = 8×15 = 120 cm

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• Now to calculate area I will use herons formula:

S = (75+105+120)/2

= 300/2

= 150

• Now AREA is:

A = √[s(s−a)(s−b)(s−c)]

= √[150(150-75)(150-105)(150-120)]

= √[150 × 75 × 45 × 30]

= √[25×2×3 × 15×5 × 15×3 × 5×3×2]

= [5×2×3 × 15× 5]

= 2250

Hence, AREA of TRIANGLE is 2250 cm²

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