3
advanced-math

The height of a triangle is 4 less than its base. If the area is 30, find the base.

A

10

B

6

C

12

D

8

Correct Answer: A

Choice A is the correct answer.

  1. Setup: Base = bb, Height = b−4b - 4. Area = 0.5×b×h0.5 \times b \times h.
  2. Equation: 0.5b(b−4)=300.5b(b - 4) = 30.
  3. Solve: b(b−4)=60⇒b2−4b−60=0b(b - 4) = 60 \Rightarrow b^2 - 4b - 60 = 0.
  4. Factor: (b−10)(b+6)=0(b - 10)(b + 6) = 0.
  5. Result: b=10b = 10 (since base must be positive).

Choice B is incorrect because area would be 0.5∗6∗2=60.5*6*2 = 6. Choice C is incorrect. Choice D is incorrect.

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