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Year 9 Interactive Maths - Second Edition
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Problem Solving
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To
find the solution to some problems in science, engineering or geometry, a quadratic
equation is formed; and then solved.
Example 6
The length of the side of a square paddock is x m. If one
side of the paddock is lengthened by 7 m and the adjacent side is
shortened by 4 m so as to make the paddock rectangular, find:
a. an expression for the area, A, of the rectangular
paddock in terms of x
b. the value of x, when the area of the rectangular
paddock is 80 m²
c. the area of the square paddock using the answer to b.
Solution:
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Example 7
A square picture is fixed in the middle of a square frame as shown in
the diagram. If the width of the border is x cm, express:
a. the length, l cm, of the frame in terms of x.
b. the area, A cm², of the frame in terms of x.
Solution:
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Example 8
A cyclist takes (x + 2) hours to travel a distance of 80
kilometres when cycling at x kilometres per hour. Find:
a. the value of x
b. the time taken to complete the journey
Solution:
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Example 9
A rectangular flower-bed 8 m by 6 m is surrounded by a concrete path,
as shown in the diagram. If the area of the path is 32 m², find:
a. the value of x
b. the width of the path |
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Solution:
a. From the diagram, we see that the outer rectangle is (8 + 2x)
metres long and (6 + 2x) metres wide.
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