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

Question

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

its area

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Piper 1 week 2022-01-15T09:44:19+00:00 2 Answers 0 views 0

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    0
    2022-01-15T09:46:02+00:00

    Given :

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

    Perimeter of the plot is 300m.

    To Find :

    • Area of the triangular plot.

    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…

    0
    2022-01-15T09:46:10+00:00

    Answer:

    Let the sides be 3a, 5a and 7a.

    Perimeter = sum of all sides

    = > 3a + 5a + 7a = 300

    = > 15a = 300

    = > a = 300/15

    = > a = 20 m

    Sides are –

    3a = 3(20m) = 60m

    5a = 5(20m) = 100m

    7a = 7(20m) = 140m

    Semi – perimeter = 300/2 = 150

    Using heron’s formula-

    = > \sqrt{150*(150-60)(150-100)(150-140)}

    = > \sqrt{150*90*50*10}

    = > \sqrt{15*9*5*10^4}

    = > \sqrt{3*5*9*5*10^4}

    = > 5*3*10^2 \sqrt3

    = > 1500\sqrt3

    Area is 1500 \sqrt3 m^2

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