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The area of an equilateral triangle with a side length of 4
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01 Sep 2020, 03:44
01 Sep 2020, 03:44
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Question Stats:
57% (00:48) correct
42% (01:01) wrong based on 33 sessions
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Quantity A |
Quantity B |
The area of an equilateral triangle with a side length of 4 |
The area of an isosceles right triangle with a hypotenuse of 4\( \sqrt{2}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
KUDOS for the right solution and explanation
Re: The area of an equilateral triangle with a side length of 4
[#permalink]
03 Sep 2020, 01:24
03 Sep 2020, 01:24
1
Area of Equilateral Triangle:
\(S^2\sqrt{3}\)/4
Given side = 4
So A = 4\(\sqrt{3}\)
Area of Isosceles Right Triangle:
A = \(\frac{1}{2}\) L * B
We know the ratio of sides:
x:x:x\(\sqrt{2}\) = L:B:H
Given, H = 4\(\sqrt{2}\)
so x\(\sqrt{2}\) = 4\(\sqrt{2}\)
x = 4
and
A = \(\frac{1}{2}\) 4 * 4
A = 8
So Quantity B is greater
\(S^2\sqrt{3}\)/4
Given side = 4
So A = 4\(\sqrt{3}\)
Area of Isosceles Right Triangle:
A = \(\frac{1}{2}\) L * B
We know the ratio of sides:
x:x:x\(\sqrt{2}\) = L:B:H
Given, H = 4\(\sqrt{2}\)
so x\(\sqrt{2}\) = 4\(\sqrt{2}\)
x = 4
and
A = \(\frac{1}{2}\) 4 * 4
A = 8
So Quantity B is greater
Re: The area of an equilateral triangle with a side length of 4
[#permalink]
03 Sep 2020, 04:49
03 Sep 2020, 04:49
1
An Equilateral triangle can be further broken into 30:60:90 triangle, then the hypotenuse will be 4, shortest side will be 2 while the medium side(height of the triangle) will be 2√3 (following the law of 30:60:90 triangle x:x√3:2x)
The the area will be 1/2*4*2√3= 4√3...
An isocles right angle triangle means 2 sided will be equal (this implies that apart from the 90 degree angle the other angles will be 45 each)
Then 45:45:90 triangle will equal x:x:x√2
Since the hypotenuse is 4 which denote x
Then the other 2 sides will be 4 each
Area = 1/2*4*4=8
Hence answer equal B
Posted from my mobile device
The the area will be 1/2*4*2√3= 4√3...
An isocles right angle triangle means 2 sided will be equal (this implies that apart from the 90 degree angle the other angles will be 45 each)
Then 45:45:90 triangle will equal x:x:x√2
Since the hypotenuse is 4 which denote x
Then the other 2 sides will be 4 each
Area = 1/2*4*4=8
Hence answer equal B
Posted from my mobile device
