Problema Solution
A rectangle has an area of 735 cm squared. It's length and width are whole numbers.
a) what are the possibilities for the 2 numbers?
b) which possibility gives the smallest perimeter?
Answer provided by our tutors
a) Since 735 = 3*5*7^2 the possibilities for the 2 numbers are (assuming the length is bigger than the width):
3 and 5*7^2 = 245 and in this case the perimeter is: P = 2(3 + 245) = 496
5 and 3*7^2 = 147 and in this case the perimeter is: P = 2(5 + 147) = 304
7 and 3*5*7 = 105 and in this case the perimeter is: P = 2(7 + 105) = 224
3*5 = 15 and 7^2 = 49 and in this case the perimeter is: P = 2(15 + 49) = 128
3*7 = 21 and 35 and in this case the perimeter is: P = 2(21 + 35) = 112
b) The smallest possible perimeter is P = 112 thus the possibility that gives the smallest perimeter is when the width is 21 cm and the length is 35 cm.