Question

1.If the lengths of the sides of a triangle are in the ratio $3:4:5$ and its perimeter is $48cm$. Find its area.
2.The sides of a triangular plot are in the ratio $3:5:7$ and its perimeter is $300m$. Find its area (Take $\sqrt{3}=1.732$)

Answer 1

$1)$ $3:4:5$

$3x+4x+5x=48$cm

$12x=48x=4$

$12cm,16cm,20cm$ are length of sides

Using herons formula

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$s=48/2=24$cm

$=\sqrt{24(24-12)(24-16)(24-20)}$

$=\sqrt{9216}$

$=96c{m}^2$

$2)$ $3:5:7$

$3x+5x+7x=300$m

$15x=300m$

$\Rightarrow x=20$m

$60m,100m,140m$ are lengths of sides of triangle

Using herons formula for area

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$s=300m/2=150$

$=\sqrt{\frac{300}{2}(150-60)(150-100)(150-140)}$

$=\sqrt{6750000}$

$=2,598.076m^2$.