Question

Mohan 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 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.​

Answer 1

⠀Corrected Question -

Mohan 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 10500 m² and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.

Stated -

• The area of field is 10500m²
• Perpendicular distance between two // sides is 100m
• Its side is parallel to and twice the side along the road.

Asked -

• The length of the side along the river.

Formula to be used -

• Area of trapezium = 1/2 × (a + b) × h

Where -

• A + B are parallel sides of trapezium.
• H stands for height.

Analysis -

⠀⠀In the question, It has been stated that there's a trapezium-shaped field where it's side is parallel to and made twice the side along the road. As given, the area of the field is 10500m² and there perpendicular distance between those parallel sides is 100m. After all, we are asked to find the length of the side along the river. So, before we need to find the one side of trapezium (roadside) as x and other opposites sides as 2x.

Solution -

First, we will note down all the given measures or look at the attachment •

⠀⠀⠀$\twoheadrightarrow$ One side of Trapezium = x m

⠀⠀⠀$\twoheadrightarrow$ Oppaosite parallel sides as = 2x m

⠀⠀⠀$\twoheadrightarrow$ Height = 100m

⠀⠀⠀$\twoheadrightarrow$ Area = 10500m²

⠀⠀⠀⠀

Now -

⠀⠀By usin' the appropriate formula of 'Area of trapezium'

Let's find the answer..

Substituting the values -

$\begin{gathered} \dashrightarrow \sf{{ \sf \red{Area_{\:(Trapezium)} = \dfrac{1}{2} \times (a + b) \times h }}}\\\\\\ \dashrightarrow \sf{10500 = \dfrac{1}{2} \times (2x + x) \times 100 }\\\\\\\dashrightarrow\sf{10500 = \:\dfrac{1}{2} \times (3x) \times 100} \\\\\\\dashrightarrow \sf{10500 = 150x}\\\\\\\dashrightarrow \sf{ x = \dfrac{10500}{150} \: \star}\\\\\\\dashrightarrow {\boxed{\sf{\red{x = 70cm}}}}\end{gathered}$

Conclusion -

⠀⠀So, — AB = 2x = 2 × 70 = 140m

Final Answer -

⠀⠀★ The length of the side along the river is 140m.

_______________________________________________________

Answer 2

Given :-

• The area of trapezium field = 10500m²
• Distance between parallel sides = 100m

To Find :-

• The length of side along the river = ?

Solution :-

To calculate the length of side along the river at first we have to be constructed in the figures. Then calculate it's parallel side by applying formula. Because calculation , we have to assume the side along the road be x and the side along the river be 2x. In the given figure CD||AB , AD||BC and DE = CF ( Distance between AB||CD) = 100m. Here AB is side which is along the river and CD is the sides which is along the road.

Construction :-

Draw perpendicular On AB such that DE_|_AB and CF_|_AB After join points D to B then two triangle formed. ∆ADB and ∆ BDC . Simply by applying formula to set up equation then calculate the value of x.

Calculation begins :-

⇒ Area of ∆ ABD + Area of ∆ BCD = Area of ABCD

⇒ 1/2 × AB × DE + 1/2 × CD × CF = 10500

⇒ 1/2 × 2x × 100 + 1/2 × x × 100 = 10500

⇒ 1/2(2x * 100 + x * 100) = 10500

⇒ 1/2(200x + 100x) = 10500

⇒ 200x + 100x = 10500 × 2

⇒ 300x = 10500 × 2

⇒ 3x = 105 × 2

⇒ x = 35 × 2

⇒ x = 70

Hence,

• The length of side along the river (2x) = 140m
• The length of side along the road (x) = 70m