Question

the length of a rectangular office room is 1m longer than is width. if its perimeter is 10m what are its dimensions?

Answer 1

let breadth be x
so, length = x+1
now,
perimeter = 2(l+b)
10 = 2(x+x+1)
10/2 = 2x+1
5-1 = 2x
4/2 = x
2 = x
so,
breadth is 2 m
length is 3 m

Answer 2

Let,
Width be W and
Length be W + 1 ----> equation 1
Perimeter of rectangle is:
2W + 2(W+1) = 10 ----> equation 2
divide both members of eq. 2 by 2, gives you:
W + (W+1) = 5
Transposing 1 into the other side of the eq. gives you:
W + W = 5 – 1
2W = 4
dividing by 2, gives you:
W = 2m ----> Width
Substitute width of 2 to eq. 1 to get the value of the length
Length = W + 1
Length = 2 + 1 = 3m

Checking answer in equation 2 by substituting values
(both sides should be equal to 10)
2 W + 2 (W+1) = 10 (equation 2)
2 (2 ) + 2 (2+1) = 10
4 + 2 (3) = 10
10 = 10

Therefore: L = 3m and Width = 2m are correct