Monday, June 1, 2020

06/01/2020 (2019: AMC 8, Problem 2)

Q: Three identical rectangles are put together to form rectangle ABCD, as shown in the figure below. Given that the length of the shorter side of each of the smaller rectangles is 5 feet, what is the area in square feet of rectangle ABCD?

[asy] draw((0,0)--(3,0)); draw((0,0)--(0,2)); draw((0,2)--(3,2)); draw((3,2)--(3,0)); dot((0,0)); dot((0,2)); dot((3,0)); dot((3,2)); draw((2,0)--(2,2)); draw((0,1)--(2,1)); label("C",(0,0),S); label("D",(3,0),S); label("B",(3,2),N); label("A",(0,2),N); [/asy]

$\textbf{(A) }45\qquad\textbf{(B) }75\qquad\textbf{(C) }100\qquad\textbf{(D) }125\qquad\textbf{(E) }150$

                   

We know that the shortest sides (so half of AC) is 5 feet. That means that the length of AC is 5 ⋅ 2 = 10 feet.

Because AC is 10 feet, the longer side of one rectangle is 10 feet. That makes the area of a smaller rectangle 5 ⋅ 10 = 50 feet².

There are 3 of those smaller rectangles, so the total area is 50 ⋅ 3 = 150 feet², making the answer E.

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