Question

A rectangle has an area of 12 square centimeters and a perimeter of 16 centimeters. Which of the following could be its dimensions?

A: 2 cm and 6 cm
B: 3 cm and 4 cm
C: 1.5 cm and 8 cm
D: 1 cm and 12 cm

Answer 1

2x6 = 12 ✔
2+2+6+6 = 16 ✔
So A is ✔

Answer 2

Option A 2 cm and 6 cm

Explanation:

A rectangle has an area of 12 square centimeters and a perimeter of 16 cm.

We have to find the dimensions of the rectangle.

Let the length of perimeter = x and width of y cm

so area = x × y = 12 ----------(1)

and perimeter = 2 (x+y) = 16

x + y = 8 ---------(2)

Now x = (8-y)

So from equation (1)

y(8-y) = 12

8y - y² = 12

y² - 8y + 12 = 0

y² - 6y - 2y + 12 = 0

y(y-6) -2 ( y - 6 ) = 0

( y-2 ) ( y-6 ) = 0 ⇒ y = z or y = 6

Now we put the values of y in equation (1)

x × y = 12

for y = 2 2x = 12

x = 6

for y = 6 6x = 12

x = 2

Therefore, possible dimensions may be 2 and 6 cm.

Option A 2 cm and 6 cm