Difference between revisions of "2022 AMC 10B Problems/Problem 2"
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<math>\textbf{(A) }3\sqrt{5}\qquad\textbf{(B) }10\qquad\textbf{(C) }6\sqrt{5}\qquad\textbf{(D) }20\qquad\textbf{(E) }25</math> | <math>\textbf{(A) }3\sqrt{5}\qquad\textbf{(B) }10\qquad\textbf{(C) }6\sqrt{5}\qquad\textbf{(D) }20\qquad\textbf{(E) }25</math> | ||
+ | |||
+ | ==Solution== | ||
+ | |||
+ | <math>AD = AP + PD = 3 + 2 =5</math> | ||
+ | |||
+ | <math>ABCD</math> is a rhombus, so <math>AD = AB = 5</math> | ||
+ | |||
+ | <math>\bigtriangleup APB</math> is a 3-4-5 right triangle, so <math>BP = 4</math>. | ||
+ | |||
+ | Area of a rhombus <math>= bh = (AD)(BP) = 5 * 4 = \boxed{\textbf{(D) }20}</math>. | ||
+ | |||
-richiedelgado | -richiedelgado |
Revision as of 16:38, 17 November 2022
Problem
In rhombus , point
lies on segment
so that
,
, and
. What is the area of
? (Note: The figure is not drawn to scale.)
Solution
is a rhombus, so
is a 3-4-5 right triangle, so
.
Area of a rhombus .
-richiedelgado