Question

The side of a triangular plot are in the ratio 3 5 7 and its perimeter is 30 m find its area

Answer 1

Answer:

Step-by-step explanation:

ratio of sides of traingle is = 3:5:7

perimeter=30

let x be the common multiple

perimeter=sum of all sides

3x+5x+7x=30

15x=30

x=2

How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6 ; ; b = 10 ; ; c = 14 ; ;  

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6+10+14 = 30 ; ;  

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 30 }{ 2 } = 15 ; ;  

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15 * (15-6)(15-10)(15-14) } ; ; T = sqrt{ 675 } = 25.98 ; ;

Answer 2

$\large{\sf{\underline{\orange{Question⇢}}}}$

The side of a triangular plot are in the ratio 3:5:7 and its perimeter is 30 m. Find its area.

____________________________

Answer :

Area of triangle = 25.98m²

step by step explanation :

Given :

• Ratios of sides of triangular plot = 3:5:7
• Perimeter of triangular plot = 30m

To finD :

• Area of this triangular plot

Solution :

$\large{\sf{↦}}$ We have to find sides of triangle before finding area of that triangle.

Formula using :

Perimeter of triangle = $\small{\sf{sum \:of \:sides}}$

Finding Sides :

GiveN sides are 3:5:7, Let's suppose the sides are as ↦

• 3x
• 5x
• 7x

$\large{\sf{↦}}$ Perimeter of triangle = sum of sides

$\large{\sf{↦}}$ 30 = 3x + 5x + 7x

$\large{\sf{↦}}$ 30 = 15x

$\large{\sf{↦}}$ x = $\small{\sf{\frac{30}{15}}}$

$\large{\sf{↦}}$ x = 2m

Hence, sides are =

• 3x = 3×2= 6m
• 5x = 5×2 = 10m
• 7x = 7×2 = 14m

Finding area :

Now we have sides of triangle are 6m, 10m and 14m. Now we can find Area of traingle by using Heron's formula :

Formula using ( Heron's formula) :

Area of traingle = $\small{\sf{\sqrt{s(s - a)(s -b )(s - c)} }}$

Where :

s = semi perimeter of triangle↦ ( 1/2 of perimeter )= 30/2 = 15m

a = first side of triangle ↦ 6m

b = second side of triangle↦ 10m

c = third side of triangle↦ 14m

||________________________||

➠ Area of traingle = $\small{\sf{\sqrt{s(s - a)(s -b )(s - c)} }}$

➠ $\small{\sf{\sqrt{15(15 - 6)(15 - 10 )(15 - 14)} }}$

➠ $\sf{\sqrt{675} }$

➠ $\large{\sf{\boxed{\green{ 25.98m²}}}}$