FIND THE MISSING SIDE OF RECTANGLE WHEN PERIMETER IS GIVEN

To find perimeter of rectangle, we use the formula 

Perimeter = 2(length + width)

By applying the known values, we can solve for unknown.

Problem 1 :

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 square feet, how many feet of fencing will be required ?

Solution :

Since it is rectangle, the opposite sides will be equal.

From the given information, we know that one of the side is 20 feet. Let x be the unknown side.

So, sides of the rectangle are x, x, 20, 20.

Area = 680

20x = 680

x = 680/20

x = 34

Length of fencing = Perimeter of the rectangular field (including three sides)

= x + x + 20

= 2x + 20

= 2(34) + 20

= 68 + 20

= 88

So, required length of fencing is 88 feet.

Problem 2 :

The ratio between the perimeter and the width of a rectangle is 5 : 1. If the area of the rectangle is 216 sq.cm. What is the length of the rectangle ?

Solution :

Perimeter = 5x and width = x

Let length = l and width = w

Perimeter : width = 5 : 1

l = 18

So, the required length is 18 cm.

Problem 3 :

A farmer wishes to start a 100 sq.m rectangular vegetable garden. Since he has only 30 m barbed wire he fences three sides of the garden letting his house compound wall act as the fourth side fencing. The dimension of the garden is.

Solution :

Let l be the length and w be the width of the rectangle.

Area of the vegetable garden = 100 sq.m

length x width = 100

l w = 100

w = 100/l ----(1)

length of fencing covering three sides = 30 m

l + l + w = 30

2l + w = 30

2l + (100/l) = 30

2l² + 100 = 30l

2l² - 30l + 100 = 0

l² - 15l + 50 = 0

(l - 10) (l - 5) = 0

l = 10 and l = 5

So, the required dimension of the rectangle is 5 m x 20 m.