Question

Find the area of a triangle whose sides are in the ratio 5:12:13 and its perimeter is 60 cm.​

Answer 1

$5x + 12x + 13x = 60$

$30x = 60$

$x = 2$

sides are 10,24,26

as ,

${10 }^{2} \times {24}^{2} = {26}^{2}$

so it's a right angled triangle...

hence ,

Area--

$\frac{1}{2} \times 10 \times 24$

$120cm2$

Hope it helped ❤️

Answer 2

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf{ \purple{step \: by \: step \: explanation}}$

Let the sides of the triangle be x .

→ 5x , 12x & 13x

Given :-

perimeter of triangle = 60 cm

°•° perimeter of triangle= sum of all sides

→ 5x + 12x + 13x = 60.

→ 30x = 60.

$\huge \sf \implies x = \frac{60}{30}$

$\huge \sf \implies \frac{ \cancel{60} \: 2}{ \cancel{30}}$

$\huge \sf{ \implies \: 2}$

Hence

sides are

→ 5x = 5 × 2 = 10cm

→ 12x = 12 × 2 = 24cm

→ 13x = 13 × 2 = 26cm

Now ,

According to question

we have to find its area

→ we will use heron's formula here

→ semi perimeter of triangle

$\sf \implies \frac{60}{2}$

$\sf \huge \implies \frac{ \cancel{60} \: 30}{ \cancel{2}}$

$\sf{ semiperimeter \: = 30cm}$

Now,

→ √s(s - a)(s - b)(s - c)

→ √30(30 - 10)(30 - 24)(30 - 26)

→ √30(20)(6)(4)

→ √14,400

→ 120 cm²

$\huge{ \pink{ \mathfrak{THANKS}}}$