Question

A carpet is laid on the floor of a room 8 m by 5 m. There is a border of
constant width all around the carpet. If the area of the border is 12 m²,
find its width
de cach 5 m wide, running​

Answer 1

Answer:

Let the width of the border is 'x' m.

And

The length and breadth of the carpet are 8 m and 5 m

area of the carpet = 8m×5m = 40m²

length of the carpet without border = (8 – 2x)

breath of the carpet without border = (5–2x)

area of the border is 12m²

area of the carpet without border (8–2x)(5–2x)

Thus ,

12= 40– (8–2x)(5–2x)

==>12= 40-(40-26x +4x²)

==>12= 26x - 4x²

==>26x 4x²= 12

Then, ==>4x² – 26x +12= 0

==>2x²– 13x +6= 0

==>(2x - 1)(x-6) = 0

==>2x - 1= 0 and x - 6 = 0

==> x = 1/2 and x = 6

Because the border cannot be wider than the entire carpet, the width of the carpet is 1/2 m i.e., 50 cm.