Question

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

Answer 1

here is ur answer...

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Answer 2

$\bold{GIVEN}$

$\mathsf{The \: sides \: of \: an \: triangular \: plot \: is \:in \: ratio \: 3:5:7 \: and \: its \: perimeter \: is \: 300 m. }$

$\mathsf{Let \: the \: common \: ratio \: be \: x }$

$\mathsf{So, \: sides \: becomes, }$

$\bold{3x }$

$\bold{5 x }$

$\bold{ 7x }$

$\mathsf{Since, \: perimeter \:is \: the \: sum \: of \: all \: sides}$

$\mathsf{So, }$

$\mathsf{3x + 5x + 7x = 300}$

$\mathsf{15x = 300}$

$\mathsf{x = \dfrac{300}{15}}$

$\huge \boxed{\mathsf{x = 20}}$

$\mathsf{So, \: sides \: of \: triangle \: will \: be, }$

$\bold{3 \times 20 = 60}$

$\bold{5 \times 20 = 100}$

$\bold{ 7 \times 20 = 140}$

$\mathsf{Since , \: no \: side \: of \: triangle \: is \: equal \: therefore \: its \: a \: scalene \: triangle . }$

$\boxed{AREA \: OF \: SCALENE \: TRIANGLE = \sqrt{s(s-a) (s-b) (s-c)}}$

$\mathsf{Where \: s \: is \: semi \: perimeter }$

$\boxed{ \mathsf{Semi \: perimeter = \dfrac{a + b + c}{2}}}$

$\mathsf{Or \: half \: of \: perimeter \: of \: triangular \: plot}$

$\mathsf{Semi \: perimeter = \dfrac{140+60+100}{2}}$

$\mathsf{Semi \: perimeter = \dfrac{300}{2}}$

$\mathsf{Semi \: perimeter = 150}$

$\mathsf{Area \: will \: be}$

$\mathsf{AREA \: OF \: SCALENE \: TRIANGLE = \sqrt{150 (150-60) (150-100) (150-140)}}$

$\mathsf{AREA \: OF \: SCALENE \: TRIANGLE = \sqrt{150 (90) (50) (10)} }$

$\mathsf{AREA \: OF \: SCALENE \: TRIANGLE = \sqrt{6750000}}$

$\boxed{\mathsf{AREA \: OF \: SCALENE \: TRIANGLE = 2598 \: m^{2}}}$