Question

Arun wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10,800 m2 and the perpendicular distance between the two parallel sides is 120m, find the length of the side along the river.

Answer 1

Answer :-

• Measure of Side along River =  m
• Measure of Side along Road =  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.

@Agamsain