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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
47% (01:24) correct
53%
(02:04)
wrong
based on 70
sessions
History
Date
Time
Result
Not Attempted Yet
For a rectangle whose diagonal is 10cm. Which of the following cannot be its area?
A. 8
B. 12
C. 20
D. 45
E. 54
Are You Up For the Challenge: 700 Level Questions
A. 8
B. 12
C. 20
D. 45
E. 54
Are You Up For the Challenge: 700 Level Questions
05 Feb 2022, 17:43
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\(a^2 + b^2 = c^2\)
\(a^2 + b^2 = 10^2\)
\(a^2 + b^2 = 100\)
\((a+b)^2 = a^2 + 2ab + b^2\)
\((a+b)^2 = 100 - 2ab\)
Plug in answers for ab (the area of rectangle).
We also know it has to be one of the extremes (8 or 54).
Let's test them:
\((a+b)^2 = 100- 2(8) = 84\) (this is a possibility)
\((a+b)^2 = 100 - 2(54) = -8 \) (this can't work)
Therefore: E
\(a^2 + b^2 = 10^2\)
\(a^2 + b^2 = 100\)
\((a+b)^2 = a^2 + 2ab + b^2\)
\((a+b)^2 = 100 - 2ab\)
Plug in answers for ab (the area of rectangle).
We also know it has to be one of the extremes (8 or 54).
Let's test them:
\((a+b)^2 = 100- 2(8) = 84\) (this is a possibility)
\((a+b)^2 = 100 - 2(54) = -8 \) (this can't work)
Therefore: E
Given a certain perimeter of a rectangle or given a length of the diagonal, the largest area can only be produced when the sides are of equal lengths (ie when a square is formed). The largest area in this case is 50. (E) is the only way to go.
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