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14 Jan 2021, 12:15
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The angles of a triangle have measures of x°, (2x)°, and (3x)°. If the side opposite the smallest angle has a length of 4 units, how many units long is the perimeter of the triangle?
(A) \(8 \sqrt{3}\)
(B) \(8 +4\sqrt{3}\)
(C) \(12 +4\sqrt{3}\)
(D) \(16 +8\sqrt{3}\)
(E) 24
(A) \(8 \sqrt{3}\)
(B) \(8 +4\sqrt{3}\)
(C) \(12 +4\sqrt{3}\)
(D) \(16 +8\sqrt{3}\)
(E) 24
14 Jan 2021, 12:48
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Since, its a triangle - sum of angles = 180
x + 2x + 3x = 180 => x = 30 deg
Hence triangle is a 30, 60, 90 triangle => sides in ratio 1 : √3 : 2
if smallest side is 4 then other two are 4 : 4√3 : 4x2
Perimeter 12 + 4√3
C)
x + 2x + 3x = 180 => x = 30 deg
Hence triangle is a 30, 60, 90 triangle => sides in ratio 1 : √3 : 2
if smallest side is 4 then other two are 4 : 4√3 : 4x2
Perimeter 12 + 4√3
C)
14 Jan 2021, 20:35
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\(x+2x+3x=180^{\circ}\)
\(x=30^{\circ}\)
\(\triangle 30^{\circ},60^{\circ},90^{\circ}\)
\(tan 30^{\circ}=\frac{AB}{BC}\)
\(\sqrt{3}=\frac{AB}{4}\)
\(AB=4\sqrt{3}\)
\(AC^2=(4\sqrt{3})^2+4^2\)
\(AC^2=16*3+16\)
\(AC=8\)
\(Perimeter = 4+4\sqrt{3}+8=12+4\sqrt{3}\)
Ans C
\(x=30^{\circ}\)
\(\triangle 30^{\circ},60^{\circ},90^{\circ}\)
\(tan 30^{\circ}=\frac{AB}{BC}\)
\(\sqrt{3}=\frac{AB}{4}\)
\(AB=4\sqrt{3}\)
\(AC^2=(4\sqrt{3})^2+4^2\)
\(AC^2=16*3+16\)
\(AC=8\)
\(Perimeter = 4+4\sqrt{3}+8=12+4\sqrt{3}\)
Ans C
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