Question

If the sides of a triangular plot is in ratio
3: 5:7 with its perimeter 300 cms. find area
of triangular plot ​

Answer 1

Step-by-step explanation:

Let the sides of a triangular field be 3x, 5x and 7x respectively.Then,

=> 3x + 5x + 7x = 300

=> 15x = 300

=> x = 20

Now sides of the triangle = 60, 100, 140

Now the area = 1/2 x base x height.

Answer 2

$\blue{\underline \bold{★ Given :}}$

1ˢᵗ side = 3x

2ⁿᵈ side = 5x

3ʳᵈ side = 7x

Perimeter of triangle = 300 cm

$\green{\underline \bold{★First \: let's \: find \: the \: sides \: of \: triangle :}}$

$\begin{gathered} \\ \tt: \implies sum \: of \: sides \: of \: triangle \: = \: perimeter \: of \: triangle\end{gathered}$

$\begin{gathered} \\ \tt: \implies 3x + 5x + 7x = 300\end{gathered}$

$\begin{gathered} \\ \tt: \implies 15x = 300\end{gathered}$

$\begin{gathered} \\ \tt: \implies x = 20\end{gathered}$

So,

1 st side = 3x = 3(20) = 60

2nd side = 5x = 5(20) = 100

3rd side = 7x = 7(20) = 140

★ Sides of the triangle is 60m , 100m , 140m

Given, Perimeter is 300cm then

semi perimeter = Perimeter/2

》300/2

》 150m

Hence semi Perimeter is 150m

Now we have to find the area of triangular plot

As we know that,

A = √s(s - a) (s - b) (s - c)

Where a is 60m , b is 100m and c is 140 and s is 150m

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

》√150 × 90 × 50 × 10 m²

》√(15 × 9 × 5) × (10)⁴

》 √15 × (3×3) × 5 (10)⁴

》 √15 × (3 × 5) × 3 × (10)⁴

》 √15 × 15 × 3 × (10)⁴

》 √(15)² × √3 × √10⁴

》 15 × √3 × (10⁴)½

》 15 × √3 × 10²

》 15 × √3 × 100

》 1500√3 m²

Hence , Area of triangular plot is 1500√3m²