Question

The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300 m. Find its area:
a)4√30
b)8√30
c)12√30
d)16√30


√

Answer 1

Answer:

B

15003m2

The sides of a the triangular plot are in the ratio 3:5:7. So, let the sides of the triangle be 3x, 5x and 7x.

Also it is given that the perimeter of the triangle is 300 m therefore,

3x+5x+7x=300

15x=300

x=20

Therefore, the sides of the triangle are 60,100 and 140.

Now using herons formula:

S=260+100+140=2300=150 m

Area of the triangle is:

A=s(s−a)(s−b)(s−c)=150(150−60)(150−100)(150−140)=150×90×50×10=6750000

=15003 m2

Hence, area of the triangular plot is 15003 m

Please mark me BRAINLIES.

Answer 2

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

Sides of a triangular plot are in the ratio 3:5:7.

Perimeter of the plot is 300m.

$\large\sf \underline\bold{ \underline{To find: }}$

Area of the triangular plot.

$\large\sf \underline\bold{ \underline{Solution: }}</p><p>$

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