I have chosen to do questions 6, 7, and 8 in the homework book on page 33.
6. The width of a rectangle is 8cm, and its diagonal is 17cm.
a) Calculate the length of the rectangle. Show your work!
c² - b² = a²
17² - 8² = a²
(17x17) - (8x8) = a²
289cm² - 64cm² = 225cm²
225cm² = c²
√225cm² = √c²
15cm² = c²
7. A quadrilateral has a width of 17cm and a length of 26cm. A diagonal is 31cm. Is the quadrilateral a rectangle? Justify your answer.
a² + b² = c²
26² + 17² = c²
(26x26) + (17x17) = c²
676cm² + 289cm² = 965cm²
965cm² = c²
√965cm² = √c²
Answer: No, the corners do not meet at right angles because 17² + 26² ≠ 31²
8. A ship leaves port heading due west. After travelling at a speed of 20 km/h for 10h, the ship makes a 90 degree turn and heads south, travelling south for 7.5 h, how far is the ship from the port? Show your work.
20 km/h for 10h west equals 200km
20 km/h for 7.5h south equals 150km
200 km² + 150km²=?
40,000km + 22,500km = 62500km
✓62,500km = 250km²
Answer: The ship is 250km² away from the port.
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