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Problem Solving and Enrichment Activities Activities Years 9-11 | |||
| Activity No:15 | Mel's Rectangle | Answers | to the Activities List |
From the information you have been given: What is the maximum length of AD?
What is the minimum length of AD?
Choose a length for AD that satisfies these conditions and accurately draw the rectangle that has the lengths in the rectangle shown above.
Measure the length of x on your drawing.
Compare your answers with other members of your class.
Does the length of x depend on the lengths of the sides of the rectangle?
If PA = 3cm, PB = 21cm, and PC = 24cm find the length of PD.
Now find PD if PA = 18cm, PB = 12cm and PC = 4cm.
Can you find a method for calculating the length of x.
Find an equation that will allow you to find the lengths of any one missing length?
Now draw any rectangle.
Choose any point P within the rectangle.
Join P to each vertex.
Measure the lengths of these lines.
Did the relationship hold for your rectangle?
The Theorem of Pythagoras states: "The area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides."
Is the same relationship true for the areas of other shapes? (Try the semicircle and other shapes.)
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