Question

The sides of trangle are in the ratio 5: 12:13 and it's perimeter is 300m it's area is?tion

Answer 1

━━━━━━━━━━━━━━━━━━━━

$\red{ \bf Question}$

• The sides of trangle are in the ratio 5: 12:13 and it's perimeter is 300m. Find area of the Traiangle.

$\underline {\underline{ \purple{ \bf Given}}}$

• Ratio of Sides ➠ 5:12:13
• Perimeter ➠ 300 m

$\underline{ \underline{\purple { \sf To \: Find}}}$

• Sides of Triangle
• Area if the Traiangle

$\underline{ \underline{\purple{ \sf Solution : }}}$

$\green{ \sf Let \: the \: Sides \: be \: 5x, 12x \: and \: 13x \: respectively}$

As, we know Perimeter is the sum of all the sides

So,

☞$\bf 5x + 12x + 13x = 300$

☞$\bf 30x = 300$

☞$\bf x = \dfrac{ \cancel{30} \cancel{0}}{ \cancel{3} \cancel{0} }$

☞$\bf x = 10$

Therefore, we got Value of x = 10

Now, Substituting Values

First Side ➠ 5x ➠ 5 × 10 ➠ 50 m

Second Side ➠ 12x ➠ 12 × 10 ➠ 120 m

Third Side ➠ 13x ➠ 13 × 10 ➠ 130 m

Now, Calculating Area

Formula Used :- $\boxed{ \pink{\sf \sqrt{s(s - a)(s - b)(s - c)} }}$

Here, s is the Semi Perimeter of the Traiangle

☞ $\boxed{ \pink{ \sf s = \frac{a + b + c}{2} }}$

Substituting Values

☞ $\boxed{\orange{ \sf s = \frac{50 + 120 + 130}{2}} }$

☞ $\boxed{ \orange{ \sf s = \cancel{\frac{300}{2} }}}$

☞ $\boxed{ \orange{\sf s = 150}}$

Therefore, we got s = 150

Now, Substituting Values on Heron's Formula

☞$\sf \sqrt{150(150 - 50)(150 - 120)(150 - 130)}$

☞ $\sf \sqrt{150 \times 100 \times 30 \times 20}$

☞ $\sqrt{ \sf 9000000}$

☞ $\sf 3000$

Thus, Area ➠ $\blue{\bf \dag \: 3000 \: m \: \dag }$

━━━━━━━━━━━━━━━━━━━━