The perimeter of a rectangular board is 70 cm. Taking its length as x cm, find its width in terms of x.

If the area of the rectangular board is 300 cm²; find its dimensions.

Given:

Perimeter of the rectangular board = 70 cm

Length = x cm

Let b be the width of the rectangular board.

Perimeter of a rectangle = 2(l + b)

⇒ 2(x + b) = 70

⇒ x + b = $\dfrac{70}{2}$

⇒ x + b = 35

⇒ b = 35 - x

Area = l x b

⇒ x $\times$ (35 - x) = 300

⇒ 35x - x² = 300

⇒ 35x - x² - 300 = 0

⇒ x² - 35x + 300 = 0

⇒ x² - 20x - 15x + 300 = 0

⇒ x(x - 20) - 15(x - 20) = 0

⇒ (x - 20)(x - 15) = 0

⇒ x = 20 or 15

Therefore, b = (35 - x)

b = 15 or 20

Hence, the width of rectangular board is (35 - x) and the dimensions of the board are 20 cm and 15 cm.