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.

Question

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.

KnowledgeBoat · Accepted Answer

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 = ⇒ x \+ b = 35 ⇒ b = 35 \- x Area = l x b ⇒ x (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.

Mathematics

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.

Mensuration

Related Questions

For the trapezium given below; find its area.

For the trapezium given below; find its area.

The area of a rectangle is 640 m². Taking its length as x m; find, in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.

The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If area of the rectangle is three times the area of the square; find the dimensions of each.

Mathematics

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.

Mensuration

Related Questions

For the trapezium given below; find its area.

For the trapezium given below; find its area.

The area of a rectangle is 640 m2. Taking its length as x m; find, in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.

The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If area of the rectangle is three times the area of the square; find the dimensions of each.

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.

The area of a rectangle is 640 m². Taking its length as x m; find, in terms of x, the width of the rectangle. If the perimeter of the rectangle is 104 m; find its dimensions.