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71% (02:17) correct
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The measure of angle MLN is 90 degrees, the length of LM is y, and the length of LN is 2y, where y > 0. If the number of units in the perimeter of triangle LMN is equal to the number of square units in the area of triangle LMN, then what is the value of y?
(A) 2 + √ 3
(B) 3 + √ 2
(C) 3 + √ 3
(D) 3 + √5
(E) 5 + √ 3
(A) 2 + √ 3
(B) 3 + √ 2
(C) 3 + √ 3
(D) 3 + √5
(E) 5 + √ 3
kungfury42
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Feb 24, 2022 11:13 am
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\(ML = y\) and \(LN = 2y\) Therefore, \(MN = √5y\)
Therefore, Perimeter \(= 3y + √5y\)
Area \(= \frac{1}{2}*ML*LN = \frac{1}{2}*y*2y = y^2\)
Since Perimeter = Area, we have
\((3 + √5)*y = y^2\) or \(y = 3 + √5\)
Hence, D.
Posted from my mobile device
Therefore, Perimeter \(= 3y + √5y\)
Area \(= \frac{1}{2}*ML*LN = \frac{1}{2}*y*2y = y^2\)
Since Perimeter = Area, we have
\((3 + √5)*y = y^2\) or \(y = 3 + √5\)
Hence, D.
Posted from my mobile device
Aug 09, 2023 8:06 am
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