Question

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

Answer 1

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

• Triangular plot are in the ratio of 3:5:7

• Perimeter is 300m.

${ \huge{ \underline{ \green{ \bf{To \: Find :}}}}}$

• Area of triangular plot ?

${ \huge{ \underline{ \red{ \bf{Solution :}}}}}$

◑ Suppose that the sides, in metres, are 3x, 5x, and 7x.

$◑{ \sf{ \: Then, we \: know \: that}}$

$➠ \: { \sf{3x + 5x + 7x = 300 \: ( Perimeter \: of \: the \: traingle )}}$

$➠ \: { \sf{Therefore, \: 15x = 300}}$

$➠ \: { \sf{x \: = \frac{300}{15} = 20}}$

$\star{ \boxed{ \pink{ \sf{x = 20}}}} \star$

$◑ \: { \sf{So \: the \: sides \: of \: the \: triangle \: are :-}}$

$➠ \: { \sf{3 \times 20 \: m = 60 \: m}}$

$➠ \: { \sf{5 \times 20 \: m = 100 \: m}}$

$➠ \: { \sf{7 \times 20 \: m = 140 \: m}}$

$◑ \: { \sf{We \: know \: that,}}$

[tex{ { \underline{ \boxed{ \orange{ \sf{perimeter \: of \: the \: traingle = \frac{a \: + \: b \: + \: c}{2} }}}}}}[/tex]

$➠ \: { \sf{ \frac{60 + 100 + 140}{2} = \cancel\frac{300}{2} = 150 \: m}}$

$◑ \: { \sf{Now, We \: know \: that,}}$

${ \underline{ \boxed { \orange{ \sf{Area \: of \: the \: triangle = \sqrt{s(s - a) \: (s - b) \: (s - c)} }}}}}$

$➠ \: { \sf{ \sqrt{150 \: (150 - 60) \: ( 150 - 100) \: (150 - 140)m {}^{2} } }}$

$➠ \: { \sf{ \sqrt{150 \times 90 \times 50 \times 10 \: m {}^{2} } }}$

$➠ \: { \sf{1500 \sqrt{3} m {}^{2} }}$

$◑ \: { \sf{Hence, \: the \: triangular \: plot \: is \: { \boxed{ \blue{ \sf{ 1500 \sqrt{3} m {}^{2} }}}}}}$

_____________________________

Answer 2

Question:

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

Given :

• Sides of triangle are in ratio 3:5:7
• Perimeter of triangle = 300m

To find :

• Area of triangle

Solution :

To find the area of triangle we need to firstly find the sides of triangle that are in ratio 3:5:7.

Let the side (a) = 3x

Let the side (b) = 5x

Let the side (c) = 7x

Perimeter of triangle = 300m

↬3x + 5x + 7x = 300

↬ 15 x = 300

↬ x = 300/15

ㅤ↬x = 20

Now,

↬ 3x = 3(20) = 60m

↬ 5x = 5(20) = 100m

↬ 7x = 7(20) = 140m

⇨Now, finding semi-perimeter of the triangle

Semi - perimeter of triangle = a + b + c /2

↬ 60 + 100 + 140 / 2

= 150

⇨Finding area using heron's formula =

Heron's formula = √s(s- a) (s - b) (s - c)

↬ √150 (150 - 60) (150 - 100) ( 150- 140)

↬ √ 150 × 90 × 50 × 10

↬ 1500√3m²

Area of triangular plot = 1500√3m²