Question

Arun wants to buy a Trapezium shaped field. Its side along a river is parallel and twice the side along the road. if the area of this field is 10800 m² and the perpendicular distance between the two parallel side is 120m. Find the length of the side along the river.​

Answer 1

Answer :-

• Measure of Side along River = 60 m
• Measure of Side along Road = 120 m

Given :-

• Area of Trapezium Field = 10800 m²
• Distance b/w Parallel Sides (Height) = 120 m

To Find :-

• Measure of Side along River =  ?
• Measure of Side along Road =  ?

Explanation :-

Let the Side along the River of the Trapezium field to be 'x' m and then the side along the Road will be '3x' m

As we know,

$\green { \boxed { \boxed { \bf : \implies \star \: Area \: of \: Trapezium = \dfrac{1}{2} \times Sum \: of \: Parallel \: Sides \times Height \: \star}}}$

Now Substituting the values,

$\sf : \: \longrightarrow \dfrac{1}{2} \times Sum \: of \: Parallel \: Sides \times Height = Area \: of \: Trapezium$

$\sf : \: \longrightarrow \dfrac{1}{2} \times (x + 2x) \times 120 = 10800$

$\sf : \: \longrightarrow (x + 2x) = \dfrac{10800 \times 2}{120}$

$\sf : \: \longrightarrow 3x = 180$

$\sf : \: \longrightarrow x = \dfrac{180}{3}$

$\red { \underline { \boxed { \sf : \: \longrightarrow x = 60 \: m }}}$

Now Substituting the value of 'x',

$\rm \star \implies Side \: along \: the \: River = x = 1(60) = \bold{60 \:m}$

$\rm \star \implies Side \: along \: the \: Road = 2x = 2(60) = \bold{120 \:m}$

Hence, the Measure of the Side along the River and the Road of the Trapezium field are 60 m and 120 m respectively.