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

Question

3 years ago

10

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:

OlgaM077 [116] · Answer 1 · 2022-12-09T06:46:55+03:00

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