SOLVING WORD PROBLEMS ALGEBRAICALLY

Problem 1 :

The perimeter of a square patio is 48 feet. What are the dimensions of the patio?

Solution :

Perimeter of a square = 48 feet

Perimeter = 4a

48 = 4a

a = 48/4

a = 12 feet

So, the dimension of the patio is 12 feet by 12 feet.

Problem 2 :

The length of a rectangle is six feet greater than the width the perimeter is 168 feet. What are the dimensions of the rectangle?

Solution :

Given, perimeter = 168 feet

Length = 6 + width

Perimeter of a rectangle = 2(length + width)

168 = 2((6 + w) + w)

168 = 2(6 + w + w)

168 = 2(6 + 2w)

168 = `12 + 4w

168 - 12 = 4w

4w = 156

w = 39

Substitute w = 39 in l = 6 + w

length = 6 + 39

length = 45

So, length = 45 feet and width = 39 feet

Problem 3 :

The length of a rectangle is 1 yard more than twice the width. The perimeter is 218 yards. What is the length and the width?

Solution :

Perimeter of rectangle = 218 yards

Length = 1 + 2w  

Perimeter of rectangle = 2(l + w)

218 = 2(1 + 2w) + w

218 = 2(1 + 2w + w)

218 = 2 (1 + 3w)

218/2 = 1 + 3w

109 = 1 + 3w

3w = 108

Width = 36 yd

Length = 1 + 2(36)

Length = 1 + 72

Length = 73 yd

So, length and width is 73 yd and 36 yd.

Problem 4 :

The width of a rectangle is 3 meters more than half of the length. The perimeter is 516 meters. What is the length and the width?

Solution :

Perimeter of rectangle = 516 meters

Width = 3 + (1/2) l  

Perimeter of rectangle = 2(l + w)

516 = 2(l + 3 + 1/2l)

516 = 2(3 + 3/2 l)

516 = 6 + 3l

3l = 510

L = 170 meters

Width = 3 + (1/2) (170)

Width = 3 + 85

Width = 88 meters

Problem 5 :

The perimeter of a triangle is 35 cm. The length of the third side is twice the length of the first side. The length of the second side is half the length of the first side. Find the lengths of the three sides.

Solution :

Perimeter of a triangle = 35 cm

Let the length of first side = x,

Length of second side = 1/2 x

Length of third side = 2x

x + 1/2 x + 2x = 35

(2x + x + 4x)/2 = 35

7x/2 = 35

7x = 70

x = 10 cm

So, the sides are

Length of first side = 10 cm

Length of second side = 1/2 x = 1/2 (10) = 5 cm

Length of third side = 2x = 2(10) = 20 cm

Problem 6 :

The shortest side of a triangle is 8 mm less than the length of the middle side. The longest side of the triangle is 10 mm more than the length of the middle side. If the perimeter of the triangle is 29 mm, find the length of each side.

Solution :

Let the middle side be x.

Shortest side = x - 8 mm

Longest side = x + 10 mm

Perimeter of a triangle = 29 mm

x + x - 8 + x + 10 = 29

3x + 2 = 29

3x = 27

x = 9 mm

So, length of shortest side = x - 8

= 9 - 8

= 1 mm

Length of middle side = 9 mm

Length of longest side = x + 10

= 9 + 10

= 19 mm

Problem 7 :

The perimeter of a trapezoid is 33 meters. The length of the left and right sides are the same. See the figure below. If the length of the top is 6 meters more than a side and the length of the bottom is 11 meters more than the length of a side. Find the length of each side, the top and the bottom.

Solution :

Given, the perimeter of a trapezoid = 33 meters

Length of left side = x

Length of right side = x

Length of top = x + 6

Length of bottom = x + 11

x + x + x + 6 + x + 11 = 33

4x + 17 = 33

4x = 16

x = 4 m

So, length of sides = 4 m

Length of top measures = x + 6

= 4 + 6 = 10 m

Length of bottom measures = x + 11

= 4 + 11 = 15 m

Problem 8 :

The perimeter of a trapezoid is 14 inches. The length of the left and right sides are the same. If the length of the bottom is twice the length of a side and the length of the top is 1 inch less than the length of a side. Find the length of each side, the top and the bottom.

Solution :

Given, the perimeter of a trapezoid = 14 inches

Length of left side = x

Length of right side = x

Length of top = x - 1

Length of bottom = 2x

x + x + x - 1 + 2x = 14

5x - 1 = 14

5x = 15

x = 3 inches

So, length of sides = 3 inches

Length of top measures = x - 1

= 3 - 1 = 2 inches

Length of bottom measures = 2x

= 2(3) = 6 inches