Question

Question:-

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

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Answer 1

Answer:

Let the sides of a triangular plot is 3x , 5x and 7x

3x + 5x + 7x = 300 m

15x = 300

x = 300/15

x = 20

then the sides of triangular plot is

3x = (3 × 20) = 60

5x = (5 × 20) = 100

7x = (7 × 20) =140

now the area of triangular plot is

Area :-

$\sqrt{s(s - a(s - b(s - c)} \\ \\ \sqrt{150(150 - 60)(150 - 100)150 - 140)} \\ 1500 \sqrt{3m {}^{2} }$

Area of triangular plot is 1500 \sqrt{3m {}^{2} }

$\:$

Answer 2

Given :-

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

To find :-

• Area of the Triangular plot.

Assumption :-

• Let ratio be in x form as 3x, 5x, 7x.

Solution :-

□ Value of x is :-

${\sf{\implies{3x + 5x + 7x = 300}}}$

${\sf{\implies{15x = 300}}}$

${\sf{\implies{x = \dfrac{300}{15}}}}$

${ \boxed{ \blue{\sf{\implies{x = 20 \: }}}}}$

□ So, length of all sides are

${\sf{\implies{3x = 3 \times 20 ={ \green{ \boxed{ \sf {60 \: m}}}}}}}$

${\sf{\implies{5x = 5\times 20 ={ \green{ \boxed{ \sf {100 \: m}}}}}}}$

${\sf{\implies{7x = 7\times 20 ={ \green{ \boxed{ \sf {140 \: m}}}}}}}$

_______________________________

Here we have given only three sides not height so, area can be found by applying Heron's Formula. Before that

Let

• a = 60 m
• b = 100 m
• c = 140 m

■ Semiperimeter of the triangle is

${\sf{ \ratio\longmapsto{ \cfrac{a + b + c}{2} }}}$

${\sf{ \ratio\longmapsto{ \cfrac{60 + 100 + 140}{2} }}}$

${\sf{ \ratio\longmapsto{ \cfrac{300}{2} }}}$

${ \boxed{ \green{\sf{ \ratio\longmapsto{ 150 \: m}}}}}$

So, Area of the Triangular Plot :-

${ \ratio\longmapsto{\bf{ \sqrt{s(s - a)(s - b)(s - c)} }}}$

Here

• s is semiperimeter
• a, b, c are sides

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

${ \ratio\longmapsto{\bf{ \sqrt{150(90)(50)(10)} }}}$

${ \ratio\longmapsto{\bf{ \sqrt{(10 \times 15)(10 \times 9)(10 \times 5)(10)} }}}$

${ \ratio\longmapsto{\bf10 \times 10{ \sqrt{( 15)( 9)( 5)} }}}$

${ \ratio\longmapsto{\bf10 \times 10{ \sqrt{( 5 \times 3)( 3 \times 3)( 5)} }}}$

${ \ratio\longmapsto{\bf10 \times 10 \times 5 \times 3{ \sqrt{ 3} }}}$

$\large{ \underline{ \boxed{ \red{ \ratio\longmapsto{\bf1500{ \sqrt{ 3} \: \: {m}^{2} }}}}}}$

So, area of the field is 1500√3 m².