Question

fig 15.4 show the innermost lane of a running track . at each end of the rectangle is a semicircle . how much distance would vikas cover in running once round the track. ​

Answer 1

Notice that the track is made of 1 rectangle and 2 semi circles.

We can take both the semi circles as 1 complete circle.

Now to find the distance he would cover running one full round, we have to calculate the perimeter of the figure.

Perimeter of the figure = perimeter of rectangle + perimeter of circle.

PERIMETER OF RECTANGLE:

PERIMETER = 2(l+b)

= 2(112+56)

= 2(168)

= 336 m

PERIMETER OF CIRCLE:

PERIMETER = 2πr

$2 \times \frac{22}{7} \times 56$

56 goes in 7 times tables (7×8 = 56)

hence perimeter of circle = 2 × 22 × 8

= 352 m

total perimeter of the figure = 336+352 -(56+56) = 576m

therefore if Vikas runs around the track once, he covers a distance of 576m

Hope it helps

have a great day

Why is 56 subtracted?

56(the length of the rectangle) is subtracted from the figure because it lies inside the figure. Perimeter refers to the boundary of the figure.

Another way to solve this sum is to not include or calculate the perimeter of the rectangle but rather add 112, 2 times instead.