2024 AMC 8 Problem 11

Attempt Problem 11 of the 2024 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2024 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

The coordinates of △ABC\bigtriangleup ABC are A(5,7),A(5, 7), B(11,7),B(11, 7), and C(3,y),C(3, y), with y>7.y > 7. The area of △ABC\bigtriangleup ABC is 12.12. What is the value of y?y?
88
99
1010
1111
1212
Answer: D
Concepts:coordinate geometrytriangle arealinear equation
Small hint:
Use ABAB as the base of the triangle
Big hint:
The height from CC to ABAB is y−7y-7
Video solution:
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Written solution:
Consider the base of the triangle to be AB‾\overline{\rm AB} which has length 11−5=611-5=6. Given that the area of the triangle is 1212, its height must be of length 2(12)6=4\dfrac{2(12)}{6}=4. Since y>7y>7, then yy must be 7+4=117+4=11.
Thus, D is the correct answer.
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