Question

The perimeter of a rectangle is 52 centimeters. Find the length and width if the length is an odd integer and the width is 3 times the next consecutive odd integer.

Answer 1

Let length of the rectangle be l

Let witdth of the rectangle be b.

Perimeter = 2*(l+b)

Given

2*(l+b) = 52. ------------(1)

Now length is an odd integer. Let it be represented as

l = 2k+1 , where k is a positive integer

Given width of the rectangle is the 3 times next consecutive odd integer( next in reference to l = 2k+1)

So b = 3*(2k+3), where k is a positive , integer

From (1) we get

2[2k+1 + 3*(2k+3)] = 52

2[2k+1 + 6k +9] = 52

2[8k +10] = 52

4[4k +5] = 52

4k + 5 = 13

4k = 8

k = 2

so length (l) = 2k +1 = 2*2 + 1 =5 cm

width b = 3(2k +3) = 3(2*2+3) = 21 cm