Algebra with Whole Numbers Word Problems. Exercise 9

Algebra with Whole Numbers

Word Problems

Exercise 9

4. The diagram shows that a rectangular paddock has a length of x metre and a breadth of y metre. It is enclosed by a fence apart from 4 gates (one on each side of the paddock)

each z metre long. Find (in terms of x, y and z)

a. the perimeter of the paddock.

b. the length of the fence which encloses the paddock.

a. the perimeter of the paddock.

b. the length of the fence which encloses the paddock.

The diagram shows that the length of a rectangle, 2x cm, is twice its breadth, x cm.

• a. Find its perimeter (in terms of x).

• b. Find x if its perimeter is 24 cm.

• c. Hence state (in cm) the length and breadth of the rectangle.

a. Find its perimeter (in terms of x).

b. Find x if its perimeter is 24 cm.

c. Hence state (in cm) the length and breadth of the rectangle.

Length = 8 cm

Breath = 4 cm

6. The diagram shows the wire framework of a cuboid. Its height is x cm, its breadth is 4 times its

height, 4x cm, and its length is 5 times its height, 5x cm.

a. Find (in terms of x) the total length of wire used to make the cuboid.

b. Find x if the total length of wire used is 200 cm.

c. Hence state (in cm) the height, breadth and length of the cuboid.

a. Find (in terms of x) the total length of wire used to make the

cuboid.

40x

b. Find x if the total length of wire used is 200 cm.

40x = 200

x = 5 cm

c. Hence state (in cm) the height, breadth and length of the cuboid.

Height = 5 cm

Breath = 20 cmLength = 25 cm

7. The diagram shows a farm gate made from tubular steel. It has a length of 12x cm, a breadth of

5x cm and diagonal stays of length 13x cm.

a. Find (in terms of x) the total length of tubular steel used to make the gate.

b. Find x if 1200 cm of tubular steel is used.

c. Hence state (in cm) the length and breadth of the gate.

a. Find (in terms of x) the total length of tubular steel used to make

the gate.

60x

b. Find x if 1200 cm of tubular steel is used.

60x = 1200

x = 20 cm

c. Hence state (in cm) the length and breadth of the gate.

Length = 240 cm

Breath = 100 cm

The diagram shows a prefabricated wooden truss.

a. Find x if the horizontal length of the truss, from A to B, is 240 cm.

b. Find (in terms of x ) the total length of wood used to make the truss.

c. Find (in cm) the total length of wood used to make the truss.

a. Find x if the horizontal length of the truss, from A to B, is 240 cm.

48x = 240

x = 5 cm

b. Find (in terms of x ) the total length of wood used to make the

truss.

105x

c. Find (in cm) the total length of wood used to make the truss.

525 cm = 5. 25 m

The diagram shows a solid cuboid to have a height of x cm, a length 3 times its height and a breadth of

twice its height.

Find (in terms of x )

a. the total length of its edges.

b. its total surface area.

c. its volume.

Find (in terms of x )the total length of its edges.

24x

Find (in terms of x )its total surface area.

Find (in terms of x ) its volume.