What is the length of a rectangular garden whose perimeter is 32cm and area 39cm2?
A
25cm
B
18cm
C
13cm
D
9cm
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
perimeter = 2(l + b) = 32
l + b = \(\frac{32}{2}\)
l + b = 16
b = 16 - 1.......(1)
Area = l + b = 39
lb = 39 .....(2)
put (1) into (2)
l(16 - 1) = 39
16l - l2 = 39
l2 = 13l - 3l + 39 = 0
l(l - 13) - 3(1 - 13) = 0
(l - 3)(l + 130 = 0
l - 3 = 0 or l - 13 = 0
l = 3cm or l = 13cm; The length in 13cm
Source: Myschool Past Questions Archive (Record #36551)