Question

A path 2.5 metre wide runs all the way round a plot of land measuring 40m long by 24m wide. What is the area of the path?

Answer 1

Answer:

Let's draw the figure (I used ms paint for the figure). From the figure:

• DA=CB=24m
• AB=CD=40m
• Path- 4.5 m wide.

We need to find the brown coloured area.

Now, Area of the plot (bigger rectangle) - l×b

⇒(40×24)m²

⇒960m²

Now, we know that the path is 2.5 m wide.

So OP=2.5m, QT=2.5m.

Together, OP+QT+PQ=AD.

We know that AD=24m, OP=2.5m, QT=2.5m.

∴2.5+2.5+PQ=24.

PQ=24-5

PQ=19 m.

Similarly, US=2.5 m, VP=2.5 m.

Together, US+VP+PS=CD.

We know that CD=40 m, US=2.5 m, VP=2.5 m.

∴2.5+2.5+PS=40

PS=35 m.

Now, area of the smaller rectangle PQRS is l×b. PS is length, PQ is breadth in PQRS.

Area = PS×PQ

=35×19

=665 m².

Area of path - Area of bigger rectangle (ABCD) - Area of smaller rectangle (PQRS)

Area = 960 - 665

= 295m²

HOPE THIS HELPS :D