Question

A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.

Answer 1

Perimeter of rectangle = 44 cm
length + breadth =  = 22 cm
Let length = x
then breadth = 22 – x
According to the condition,
x(22 - x) = 105
⇒ 22x - x² = 105
⇒ x² - 22x + 105 = 0
⇒ x² - 15x - 7x + 105 = 0
⇒ x(x - 15) -7(x - 15) = 0
⇒ (x - 15)(x - 7) = 0
Either x - 15 = 0,
then x = 15
or
x - 7 = 0,
then x = 7
As length > breadth,
x = 7 is not admissible.
∴ Length = 15cm
and breadth 
= 22 - 15
= 7cm.