5 Solving Equations

From the first four sections you can see that any quantity can be worked out by using the appropiate formula and doing what the formula says, often multiplication and/or addition, but also powers, subtraction and/or division.

But what if you need to find the width of a rectangle when the area and the length are known.

Eg. What is the width of a rectangle which has an area of 90cm² and a length of 16cm?

The required formula is the same :  		A = lw

Substituting the numbers gives.		       	90 = 16w

That is 16 x width = 90. To find what number to multiply 16 by to get 90, divide 90 by 16

				          90 ÷ 16 = w

				      	   w = 5.625cm

5A Use the formula A=lw to find the width of these rectangles.

1. Area=20cm², length=5cm 	 2. Area=50cm², length=12cm 	 3. Area=24.5cm², length=7cm

5B Exactly the same method is used to solve these equations.

      Although you may recognise some of them you do not need to know what they are for.

1. A=lw find l when A=50, w=8			6. P=4l find l when P=30

2. F=ma find a when F=90, m=12 		7. h=ac find a when h=12, c=0.5

3. a=bh find b when a=72, h=9 			8. v=gt find g when v=71, t=12

4. d=st find s when t=3.5, d=15 			9. W=mg find m when W=96,g=9.8

5. C=pd find d when C=125 		       		10. T=fr find r when T=59.5, F=3.5

5C Use the formula d=st to work out:-

1. distance travelled by a train which travels at 60 mph for 4 hours.

2. speed of a car which travels 130 miles in 3 hours.

3. time taken to travel 220 miles at a speed of 45 mph.

5D use the foemula F=pa (Force = pressure X area) to find:-

1. force when a pressure of 3 N/m² is applied over an area of 4m²

2. pressure when a force of 7N is applied to an area of 3m²

3. area on which a force of 17N is applied to produce a pressure of 12N/m²

A more complicated example: Find the length of a rectangle which has a perimeter of 30cm and a width of 3cm.

Write down the formula 		P=2l+2w

Substitute the numbers 		30=2l+(2x3)

Do the calculation 			30=2l+6

.				24=2l

				l = 12cm

5E Work out the length of the rectangles which have:-

1. Perimeter 20cm, width 4cm

2. Perimeter 28cm, width 3cm

3. Perimeter 50cm, width 12cm.

4. Perimeter 30cm, width 4.5cm

5. Perimeter 47cm, width 8.4cm

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