Question

the sides of a traingle are in the rario 3: 4: 5 . if its perimeter is 36 then what is its area
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Answer 1

Step-by-step explanation:

let the side be x

3x+4x+5x=36

12x=36

x=3

sides are=9,12,15

s=a+b+c/2=36/2=18

area=√s(s-a)(s-b)(s-c)

√18(18-9)(18-12)(18-15)

√18×9×6×3

√9×2×9×2×3×3

9×2×3

54

Answer 2

Given :

• Ratio given 3:4:5
• Perimeter

To find :

• Area of triangle

According to the question,

Let the sides be 3x,4x and 5x

And perimeter is 36 cm

→ 3x + 4x + 5x = 36 cm

→ 12x = 36 cm

→ x = 36 ÷ 12

∴ x = 3 cm

Value of 3x :

→ 3x

→ 3(3)

→ 9 cm

Value of 4x :

→ 4x

→ 4(3)

→ 12 cm

Value of 5x :

→ 5x

→ 5(3)

→ 15 cm

Now we will find area of triangle by Heron's formula :

→ Sides are 9 cm,12 cm and 15 cm

$\implies \sf{ \dfrac{a + b + c}{2} } \\ \implies \sf{ \dfrac{9 + 12 + 15}{2} } \\ \implies \sf{ \dfrac{36}{2} = 18 \: cm }$

$\implies\sf{ \sqrt{s(s - a)(s - b)(s - c)} } \\ \\ \implies \sf{ \sqrt{18(18 - 9)(18 - 12)(18 - 15)} } \\ \\ \implies \sf{ \sqrt{18(9)(6)(3)} } \\ \\ \implies \sf{ \sqrt{6 \times 3 \times 3 \times 3 \times 6 \times 3} } \\ \\ \implies \sf{6 \times 3 \times 3} \\ \\ \implies \sf{54 \: {cm}^{2} } \green \bigstar$