# Problems involving lengths and Distances

The length of a rectangle is 6 units more than its breadth. Its perimeter is 20 units. Find its length and breadth.

Let the breadth of the rectangles be x units.

Then length = x + 6** **units.

2 (length + breadth) = perimeter

Since the perimeter is 20 units,

therefore length + breadth = 10 units.

Hence x + (x + 6) = 10 or 2x + 6 =10

.^{.}. 2x = 4, or x = 2

Breadth = 2 units;

length = 2 + 6 = 8 units. Length = 8 units.

The distance between two places A and B is 240 km. A motorcyclist starts from A and a pedestrian starts from B at the same time. The speed of the motorcyclist is 15 times that of a pedestrian. Three hours after they start, they meet at a point M. How far is this point from A and B?

It is always helpful, if you draw a figure to show your problem.

Total distance is 240 km.

** ** 15 x km/h for 3 h x km/h for 3h

Let the speed of the pedestrian be x km per hour.

Total distance = 240 km

Distance covered by Pedestrian + Distance covered by motorcyclist = 240 km

45

*x*+ 3

*x*= 240

48

*x*= 240

x = 5

They will meet at the point M, which is 15 km from B and 225 km from A.