GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The area of an equilateral triangle with a side length of 4
[#permalink]
01 Sep 2020, 03:44
01 Sep 2020, 03:44
Expert Reply
00:00
Question Stats:
55% (00:48) correct
44% (00:58) wrong based on 34 sessions
Hide Show timer Statistics
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
