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What is the area of a triangle that has two sides that each
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10 Aug 2020, 10:07
10 Aug 2020, 10:07
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What is the area of a triangle that has two sides that each have a length of 10, and whose perimeter is equal to that of a square whose area is 81?
A. 30
B. 36
C. 42
D. 48
E. 60
A. 30
B. 36
C. 42
D. 48
E. 60
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Joined: 10 Apr 2015
Posts: 6218
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Re: What is the area of a triangle that has two sides that each
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11 Aug 2020, 08:03
11 Aug 2020, 08:03
1
Carcass wrote:
What is the area of a triangle that has two sides that each have a length of 10, and whose perimeter is equal to that of a square whose area is 81?
A. 30
B. 36
C. 42
D. 48
E. 60
A. 30
B. 36
C. 42
D. 48
E. 60
If a square has AREA 81, then each side of that square has length 9 (since 9 x 9 = 81)
So the PERIMETER of that square = 9 + 9 + 9 + 9 = 36
The triangle that has two sides that each have a length of 10, and whose perimeter is equal to that of a square whose area is 81
So the perimeter of the triangle = 36
If we let x = the length of the triangle's unknown side, we can write: 10 + 10 + x = 36
Solve, to get x = 16
So, the triangle has lengths 10, 10, 16 and we want to determine the area of this triangle.
Here's what we're dealing with:
Since we have an isosceles triangle, the altitude becomes the perpendicular bisector of the base.
As you can see, the altitude divides the triangle into two EQUAL RIGHT triangles
So, we can apply the Pythagorean Theorem to determine that the missing side has length 6
In other words, the triangle has height 6 and base 16
Area of triangle = (base)(height)/2 = (16)(6)/2 = 48
Answer: D
Cheers,
Brent
gmatclubot
Re: What is the area of a triangle that has two sides that each [#permalink]
11 Aug 2020, 08:03
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