Question

The sides of a triangle are in the ratio 3:5:7 and its perimeter is 300 m. Find its area

Answer 1

Answer:

Given:-

The perimeter of a triangle is 300 m. If its sides are in the ratio 3:5:7.

Find:-

Find the area of the triangle .

As per the given request let us assume.

Side (1) = 3x

Side (2) = 5x

Side (3) = 7x

We know that:-

= Sum of all sides = 300

= 3x + 5x + 7x = 300

= 20

Hence, the three semi-perimeter are:-

3 × 20 = 60.

5 × 20 = 100.

7 × 20 = 140.

Using formula:-

Area = √s(s - a) (s - b) (s - c)

Calculations:-

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

= 150 (90 × 50 × 10)

= 1500 √3 m²

Therefore this is the required answer.

Answer 2

$\huge{\underline{\sf{Question :-}}}}$

The sides of a triangle are in the ratio 3:5:7 and its perimeter is 300 m. Find its area.

$\huge{\underline{\sf{Answer :-}}}}$

$\sf Given\begin{cases} &\sf{Perimeter\;of\;the\; triangle\;=\be{300\:m}}\\&\sf{Ratio\;of\;the\;sides\: of\: the\: traingle=\;\bf{3:\:5:\:7}}\end{cases}$

$\boxed{ \sf \blue{ To \: Find : }}$

• Area of the triangle = ❓

$\green{\underline\bold{Given,}}$

✏ Let the first side of the triangle,a = '3x'

✏ Let the second side of the triangle,b = '5x'

✏ Let the third side of the triangle,c = '7x'

$\pink{\underline\bold{According\: to\: the\: question ,\:}}$

⇒300 = 3x + 5x + 7x

⇒300 = 15x

⇒15x = 300

⇒x = $\frac{300}{15}$

⇒x = 20

$\green{\underline\bold{Now,}}$

✯ Putting the value of x. We get:

• First side of the triangle,a = '3x' = 60
• Second side of the triangle,b = '5x' = 100
• Third side of the triangle,c = '7x' = 140

$\green{\underline\bold{We \:know\:by\:applying\:Heron's \:formula,}}$

$\boxed{ \sf \blue{ Area=\sqrt{s(s-a)\times(s-b)\times(s-c)}}}$

$\green{\underline\bold{Where,}}$

s = semi-perimeter = $\frac{300}{2}$ = 150

a = 60, b = 100, c = 140

$\green{\underline\bold{Again,}}$

$Area\: = \sqrt {150(150-60)\times(150-100)\times(150-140)}$

⇒$\sqrt {150(90)\times(50)\times(10)}$

⇒1500√3 m sq.

$\pink{\underline\bold{∴\: Area \:of \:the\: triangle \:= \: 1500\sqrt{3 }\:m\:sq..}}$

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