The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is
Question:
The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is
The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is
Options
Answer: (4) √7
Explanation:
Let BD=x, then DC=3-x. Area ratio: Area(ADC)/Area(ABD)=DC/BD=1/2, so (3-x)/x=1/2, giving x=2, DC=1. Using coordinate geometry or distance formula with D at distance 2 from B along BC, we can calculate AD=√7.
Explanation:
Let BD=x, then DC=3-x. Area ratio: Area(ADC)/Area(ABD)=DC/BD=1/2, so (3-x)/x=1/2, giving x=2, DC=1. Using coordinate geometry or distance formula with D at distance 2 from B along BC, we can calculate AD=√7.
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