Diagram 5 shows a triangle ABD such that AD = 17 cm, AB = 10 cm and BD = 21 cm. The straight line AC is perpendicular to the str
aight line BD and the value of area of triangle ABD is an integer. Calculate the length of AC, in cm. (4 marks)
1 answer:
Answer:
8
Step-by-step explanation:
100 = x^2 + AC^2
17^2 = AC^2 + (21 - x)^2
289 = AC^2 + 21^2 + x^2 - 2*21*x
289 =<u> AC^2</u> + 441 +<u> x^2</u> - 42x
from 1st equation AC^2 + x^2 = 100
289 = 441 + 100 - 42x
289 = 541 - 42x
42x = 541 - 289 = 252
x = 252/42 = 6
so AC^2 = 100 - 6^2 = 100 - 36 = 64
AC = 8
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