Question

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

Answer 1

Given, perimeter of rectangle = 44 cm and area of rectangle = 105 cm²

Also, length of rectangle is given equal to x cm.

Now, perimeter of rectangle = 2 (length + breadth) = 44

⇒ 2 (x + breadth) = 44

⇒ x + breadth = 22

⇒ breadth of the rectangle = 22 - x

Again, area of rectangle = 105 cm²

⇒ length × breadth = 105

⇒ x × (22 - x) = 105
⇒ 22x - x² = 105
⇒ x² - 22x + 105 = 0

⇒ x² - 15x - 7x + 105 = 0

⇒ (x - 15)(x - 7) = 0

⇒ x = 15 or 7

When x = 15, breadth of the rectangle = 22 - x = 22 - 15 = 7 cm

and when x = 7, breadth of the rectangle = 22 - x = 22 - 7 = 15 cm