A and B are two fixed points 10 cm apart. C is a point on AB such that AC = 4 cm. If the length of AC is increased by 20%, the length of BC will decrease by:20%15.5%13.3%12%
Question
A and B are two fixed points 10 cm apart. C is a point on AB such that AC = 4 cm. If the length of AC is increased by 20%, the length of BC will decrease by:20%15.5%13.3%12%
Solution
The initial length of AC is 4 cm. If it is increased by 20%, the new length of AC will be 4 cm + 20/100 * 4 cm = 4.8 cm.
The initial length of AB is 10 cm. Since A and B are fixed points, this length doesn't change. Therefore, the length of BC is always AB - AC.
Initially, BC = AB - AC = 10 cm - 4 cm = 6 cm.
After AC is increased, BC = AB - AC = 10 cm - 4.8 cm = 5.2 cm.
The decrease in the length of BC is the initial length minus the new length, which is 6 cm - 5.2 cm = 0.8 cm.
To find the percentage decrease, we divide the decrease by the initial length and multiply by 100:
Percentage decrease = (0.8 cm / 6 cm) * 100 = 13.3%.
So, the length of BC will decrease by 13.3%.
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