Question

the primeter of a triangle ground is 900find it's sides in ration 3:5:4using h. f . find the area of the ground?
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Answer 1

Diagram:-

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){ \bf A }\put(0.5,-0.3){ \bf C }\put(5.2,-0.3){ \bf B }\end{picture}$

Let the sides are

• 3x ,4x , 5x

Perimeter=900

$\qquad\quad {:}\longmapsto\sf Semi perimeter=s={\dfrac {900}{2}}=450$

• According to Heron 's Formula

$\boxed{\sf s={\dfrac {a+b+c}{2}}}$

• Substitute the values

$\qquad\quad {:}\longmapsto\sf {\dfrac {3x+4x+5x}{2}}=450$

$\qquad\quad {:}\longmapsto\sf {\dfrac {13x}{2}}=450$

$\qquad\quad {:}\longmapsto\sf 13x=900$

$\qquad\quad {:}\longmapsto\sf x={\dfrac {900}{13}}$

$\qquad\quad {:}\longmapsto\sf x=69.2$

$\qquad\quad {:}\longmapsto\sf x=69 (Approx)$

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$\qquad\quad {:}\longmapsto\sf 3x=3×69=207$

$\qquad\quad {:}\longmapsto\sf 4x=4×69=276$

$\qquad\quad {:}\longmapsto\sf 5x=5×69=345$

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• According to Heron 's Formula

$\boxed{\bf Area=\sqrt {s (s-a)(s-b)(s-c)}}$

• Substitute the values

$\qquad\quad {:}\longmapsto\sf Area=\sqrt {450 (450-207)(450-276)(450-345)}$

$\qquad\quad {:}\longmapsto\sf Area=\sqrt {450×243×174×105}$

$\qquad\quad {:}\longmapsto\sf Area=\sqrt {2,244,469,500}$

$\qquad\quad {:}\longmapsto\sf Area=47,375.8$

$\qquad\quad {:}\longmapsto\sf Area=47,375 units {}_{(Approx)}$

$\therefore{\underline{\boxed{\sf Area=47,375units.}}}$