Question

A rectangular lot is 100 meters wide and 150 meters long.

Answer 1

Answer:

A rectangular lot is 100 meters wide and 150 meters long.Give the length and width of another rectangular lot that has the same perimeter but a smaller area.

The rectangular lot is having length of 170 meters and width of 80 meters.

Step-by-step explanation:

Given:

A rectangle.

Length of the rectangle = 150 meters

Width of the rectangle =100 meters

So perimeter of this rectangle = 2 (width+ length)

And area of this rectangle =(width)(length)

• Perimeter = $2(w+l)$

                         = $2(150+100)$

                         = $500$ meters.

• Area = $2(w)(l)$

                = $2\times 100\times 150$

                = $30000$ square meters.

Now we have to find an another rectangular lot which has the same perimeter but different area.

Note: Subtract 20 m from the width and add 20m length into the longer side. (We can try with another multiple of 10).

So,

The new width = 100-20 = 80 meters.

And the new length =150+20 = 170 meters.

Lets check the perimeter and its area.

The perimeter must be equivalent to 500 meters and its area be less than 30000 sq-meters.

• Perimeter = $2(w+l)$

                          = $2(80+170)$

                          = $500$ meters.

• Area = $(w)(l)$

                 = $(80)(170)$

                 = $13600$ square meters.

Hence the rectangular lot with length 170 m and with 80 m proves to have same perimeter and smaller area.