Hello,
Can you please assist with this:
Which of the following could be the area of an isosceles triangle with perimeter l8 and one side
of length 8 ?
(A) 6
(B) 12
(C) 14
(D) 16
(E) 18
OA: B
I tried to solve as follows:
Since in any triangle the third side must be less than the sum of the other 2 sides we can have here:
5 + 5 > 8 - Case 1
8 + 2 > 8 - Case 2
In both these cases the perimeter is 18. However, I think in Case 2, the angle opposite 2 would be 90 degrees and since it is greatest angle in this triangle it cannot face 2.
So I am thinking that the sides of the triangle are 5, 5 and 8. However I am not sure if this is correct since it doesn't look right when I plug in the values for the 45:45:90 angles.
Can you please assist?
Thanks,
Sri
Length of an isoscles triangle
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Hey Sri,gmattesttaker2 wrote:Hello,
Can you please assist with this:
Which of the following could be the area of an isosceles triangle with perimeter l8 and one side
of length 8 ?
(A) 6
(B) 12
(C) 14
(D) 16
(E) 18
Don't worry about this question. It requires us to use something called Heron's formula (sometimes called Hero's formula). More here: https://www.mathsisfun.com/geometry/herons-formula.html
Knowledge of this formula is NOT REQUIRED on the GMAT.
What's the source of this question?
Cheers,
Brent
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Hello Brent,Brent@GMATPrepNow wrote:Hey Sri,gmattesttaker2 wrote:Hello,
Can you please assist with this:
Which of the following could be the area of an isosceles triangle with perimeter l8 and one side
of length 8 ?
(A) 6
(B) 12
(C) 14
(D) 16
(E) 18
Don't worry about this question. It requires us to use something called Heron's formula (sometimes called Hero's formula). More here: https://www.mathsisfun.com/geometry/herons-formula.html
Knowledge of this formula is NOT REQUIRED on the GMAT.
What's the source of this question?
Cheers,
Brent
Thank you very much for the clarification. This question is a part of a question set that I got for practice problems. Unfortunately they don't have the detailed solutions. Just the answer. Thanks for all your help.
Best Regards,
Sri
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- Scott@TargetTestPrep
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Since the isosceles triangle has a perimeter of 18 and a side length of 8, we could have the following sides:gmattesttaker2 wrote:Which of the following could be the area of an isosceles triangle with perimeter l8 and one side of length 8 ?
(A) 6
(B) 12
(C) 14
(D) 16
(E) 18
1) 8, 8, 2
or
2) 8, 5, 5
In option 1, the base is 2 and the legs (the sides that have equal length) are 8 each. The height of this triangle, h, satisfies the Pythagorean theorem in the form (b/2)^2 + h^2 = l^2 where b is the base and l is a leg of the isosceles triangle. Thus:
(2/2)^2 + h^2 = 8^2
1 + h^2 = 64
h^2 = 63
h = √63
Recall that the area of a triangle is (b x h)/2, so the area of the triangle is (2 x √63)/2 = √63. However, this is not one of the answer choices. Thus, we must consider option 2.
In option 2, the base is 8 and the legs are 5 each. So, we have:
(b/2)^2 + h^2 = l^2
(8/2)^2 + h^2 = 5^2
16 + h^2 = 25
h^2 = 9
h = √9 = 3
So, the area of the triangle is (8 x 3)/2 = 24/2 = 12.
Answer: B
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