Question

The length of a rectangular park is thrice its breadth. If Seema jogged around it 2 times and covered a distance of 4 km. What is the length of the park?

Answer 1

Answer:

The length of the park is 3/4 km (or 0.75 km).

Step-by-step explanation:

"Thrice its breadth" is a fancy way of saying three times the width. Therefore, we can make the equation for the width of the park be p. The length will be represented by 3p.

First let's find the perimeter of the park by using the formula 2(w + L), which is multiplying both the width and length by two and then adding them together.

2(p + 3p) = perimeter

2p + 6p = 8p; after distributing 2 inside the parentheses and combining like terms you are left with 8p as the perimeter.

Now this is where Seema jogging around the park and the distance covered comes into play.

We can make the perimeter equal to 4 km/2 because this is the perimeter of the park (since Seema ran around it twice, we divide by 2 to make it like she only ran around it once).

Make our expression for the perimeter equal to the actual perimeter.

8p = 2 (4/2)

Divide both sides of the equation by 8 to isolate and solve for p, the length of the park.

p = 2/8; simplified it becomes p = 1/4.

Substitute x into the expression representing the length: 3p.

3(1/4) = 3/4 or 0.75; this is the length of the park.

Answer 2

$\textbf{\underline{\underline{Answer :-}}}$

The Length of the Rectangle is 0.75 km and Breadth is 0.25 km.

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

Length of the Rectangle = Thrice its breadth.

Seema jogged around = 2 times

Covered distance of = 4 km

To find :

The Length of Rectangle

Solution :

As she takes a round along the boundary 2 times, the distance covered will be the twice of the the Perimeter by her.

$\rule{300}{1.5}$

Divide 4 by 2 to get the Perimeter :

$\tt{\implies} \: 4 \div 2$

$\tt{\implies} \: 2$

2 km is the Perimeter of the Rectangle

$\rule{300}{1.5}$

As we got the Perimeter, we can now find the dimensions of the Rectangle.

Consider Breadth as x

Length = 3x

★ $\boxed{\sf{Perimeter = 2(Length+Breadth)}}$

$\tt{\implies} \: 2(3x + x) = 2$

$\tt{\implies} \: 6x + 2x = 2$

$\tt{\implies} \: 8x = 2$

$\tt{\implies} \: x = \dfrac{2}{8}$

$\tt{\implies} \: x = 0.25$

$\rule{300}{1.5}$

Value of 3x

$\tt{\implies} \:3 \times 0.25$

$\tt{\implies} \: 0.75$

$\therefore$ The Length of the Rectangle is 0.75 km and Breadth is 0.25 km

$\rule{300}{1.5}$

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies} \: 2(0.75 + 0.25) = 2$

$\tt{\implies} \: 1.5 + 0.5 = 2$

$\tt{\implies} \: 2 = 2$

$\therefore$ The Length of the Rectangle is 0.75 km and Breadth is 0.25 km.