Question

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

its area
​

Answer 1

━━━━━━━━━━━━━━━━━━━━━━━━━

$\large \bold{\underline{\sf{\blue{Given}}}}$

• Sides of a triangular plot are in the ratio 3:5:7.
• Perimeter of the plot is 300m.

$\large \bold{\underline{\sf{\pink{To\:Find}}}}$

• Area of the triangular plot.

$\large \bold{\underline{\sf{\red{Solution}}}}$

Firstly we will find the sides of triangular plot :

$\longmapsto\tt\bold{Let\:sides\:be=3x,5x\:and\:7x}$

$\longmapsto\tt{3x+5x+7x=300}$

$\longmapsto\tt{15x=300}$

$\longmapsto\tt{x=\cancel\dfrac{300}{15}}$

$\longmapsto\tt\bold{x=20}$

So , The sides of Triangular plot are 60m , 100m and 140m.

Now ,

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{\dfrac{60+100+140}{2}}$

$\longmapsto\tt{\cancel\dfrac{300}{2}}$

$\longmapsto\tt\bold{150m.}$

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{150(150-60)(150-100)(150-140)}}$

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

$\longmapsto\tt{\sqrt{3\times{5}\times{5}\times{2}\times{3}\times{3}\times{5}\times{2}\times{5}\times{2}\times{5}\times{5}\times{2}}}$

$\longmapsto\tt{3\times{5}\times{5}\times{5}\times{2}\times{2}\sqrt{3}}$

$\longmapsto\tt\bold{1500\sqrt{3}{m}^{2}}$

Therefore , The Area of the Triangular Plot is 1500√3m²...

━━━━━━━━━━━━━━━━━━━━━━━━━

${\huge{\underline{\small{\mathbb{\blue{HOPE\:HELP\:U\:BUDDY :)}}}}}}$

${\huge{\underline{\small{\mathbb{\pink{</p><p>~cαndчcαnє♡ :)}}}}}}$

$\huge\underline\bold\orange{тнαηkyσυ}$

Answer 2

Answer:

Let the sides of the triangle be 3x, 5x and 7x repsectively and since the perimeter is 300m

So, 3x + 5x + 7x=300

15x=300

x=300/15

x=20 m

so,length of one side=60 m

length of second side=100 m

and length of third side=140 m

Now perimeter=300m

therefore semi-perimeter=150 metre

now according to herons formula -

Area = root 150* (150-60) * (150-100) * (150-140)

= root 150 * 90 * 50 * 10

= root 30*5 * 30*3 * 5*10 *10

= root 30^2 * 5^2 * 10^2 *3

= 30 * 5 * 10 * root 3

= 1500 root 3