Question

8. The sides of a triangle are in the ratio of 3 : 5 : 7 and its perimeter is 300 cm. Its area will be:

1000√3 sq.cm

1500√3 sq.cm

1700√3 sq.cm

1900√3 sq.cm​

Answer 1

Answer :

$1500 \sqrt{3}$

explanation: it is there in the given pic

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

The sides of a triangle are in the ratio of 3:5:7 & it's perimeter is 300 cm .

$\underline{\bf{Explanation\::}}$

Firstly, attachment a figure of triangle according to the question .

Let the sides of a triangle are in the ratio be r .

As we know that formula of the perimeter of triangle;

$\boxed{\bf{Perimeter \:of\:\triangle = Side+Side +Side}}$

A/q

$\mapsto\tt{3r + 5r + 7r = 300}$

$\mapsto\tt{15r = 300}$

$\mapsto\tt{r = \cancel{300/15}}$

$\mapsto\bf{r=20\:cm}$

Now;

• 1st side of triangle = 3r = (3 × 20) cm = 60 cm .
• 2nd side of triangle = 5r = (5 × 20) cm = 100 cm .
• 3rd side of triangle = 7r = (7 × 20 ) cm = 140 cm .

$\underline{\mathcal{\red{USING\:\:HERON'S\:\:FORMULA\::}}}$

$\longrightarrow\tt{Semi-perimeter = \dfrac{Side+Side+Side}{2} }$

$\longrightarrow\tt{Semi-perimeter = \dfrac{60+100+140}{2} }$

$\longrightarrow\tt{Semi-perimeter = \cancel{\dfrac{300}{2} }}$

$\longrightarrow\tt{Semi-perimeter = 150\:cm}$

Now;

$\mapsto\tt{Area\:of\:triangle = \sqrt{s(s-a)(s-b)(s-c)} }$

$\mapsto\tt{Area\:of\:triangle = \sqrt{150(150-60)(150-100)(150-140)} }$

$\mapsto\tt{Area\:of\:triangle = \sqrt{150(90)(50)(10)} }$

$\mapsto\tt{Area\:of\:triangle = \sqrt{3\times 2\times 5\times 5 \times 3 \times 3\times 2 \times 5 \times 2 \times 5 \times 5 \times 2 \times 5} }$

$\mapsto\tt{Area\:of\:triangle =2 \times 2\times 3 \times 5 \times 5 \times 5 \sqrt{3} }$

$\mapsto\bf{Area\:of\:triangle =1500 \sqrt{3} \:cm^{2}}$

Thus;

The area of triangle will be 1500√3 cm² .