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Algebra with Whole Numbers Word Problems

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Exercise 9

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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.

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a. the perimeter of the paddock.

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

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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.

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

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b. Find x if its perimeter is 24 cm.

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c. Hence state (in cm) the length and breadth of the rectangle. Length = 8 cm Breath = 4 cm

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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.

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a. Find (in terms of x) the total length of wire used to make the cuboid. 40x

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b. Find x if the total length of wire used is 200 cm. 40x = 200 x = 5 cm

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c. Hence state (in cm) the height, breadth and length of the cuboid. Height = 5 cm Breath = 20 cm Length = 25 cm

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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.

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a. Find (in terms of x) the total length of tubular steel used to make the gate. 60x

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b. Find x if 1200 cm of tubular steel is used. 60x = 1200 x = 20 cm

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c. Hence state (in cm) the length and breadth of the gate. Length = 240 cm Breath = 100 cm

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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.

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a. Find x if the horizontal length of the truss, from A to B, is 240 cm. 48x = 240 x = 5 cm

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b. Find (in terms of x ) the total length of wood used to make the truss. 105x

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c. Find (in cm) the total length of wood used to make the truss. 525 cm = 5. 25 m

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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.

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Find (in terms of x ) the total length of its edges. 24x

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

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Find (in terms of x ) its volume.

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