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Which of the following could be the area of an isosceles triangle with
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01 Sep 2017, 01:01
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Which of the following could be the area of an isosceles triangle with
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01 Sep 2017, 01:10
Bunuel wrote: Which of the following could be the area of an isosceles triangle with perimeter 18 and one side of length 8?
(A) 6 (B) 12 (C) 14 (D) 16 (E) 18 If the triangle is isosceles, 2 sides are have equal lengths We know that the perimeter of the triangle is 18, 2x + y = 18 where x is the length of the 2 sides with equal lengths and y is the length of the other side Now, we know that one of the sides is 8 There are two possibilities, when x = 8 or y =8 If x = 8, the three sides are 8,8,2 The area calculated by Heron's formula is not part of the list of the answer options If y = 8, the three sides are 5,5,8 The area is \(2*\frac{1}{2}*4*3\) as it will form 2 right triangles with sides 3,4,5 Therefore, the area must be 12(Option B)
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Which of the following could be the area of an isosceles triangle with
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01 Sep 2017, 01:19
pushpitkc wrote: Bunuel wrote: Which of the following could be the area of an isosceles triangle with perimeter 18 and one side of length 8?
(A) 6 (B) 12 (C) 14 (D) 16 (E) 18 If the triangle is isosceles, 2 sides are have equal lengths We know that the perimeter of the triangle is 18, 2x + y = 18 where x is the length of the 2 sides with equal lengths and y is the length of the other side Now, we know that one of the sides is 8 There are two possibilities, when x = 8 or y =8 If x = 8, the three sides are 8,8,2 which is not possible(does not obey the properties of triangles) If y = 8, the three sides are 5,5,8 The area is \(2*\frac{1}{2}*4*3\) as it will form 2 right triangles with sides 3,4,5 Therefore, the area must be 12(Option B)Can u explain y 8,8,2 is not a valid triangle Sent from my A0001 using GMAT Club Forum mobile app



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Re: Which of the following could be the area of an isosceles triangle with
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01 Sep 2017, 01:31
Area of useless triangle is = a/4 x underroot of 4b2a2 so it's and will be 12 Sent from my Redmi 4A using GMAT Club Forum mobile app



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Which of the following could be the area of an isosceles triangle with
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Updated on: 01 Sep 2017, 01:50
pushpitkc wrote: Bunuel wrote: Which of the following could be the area of an isosceles triangle with perimeter 18 and one side of length 8?
(A) 6 (B) 12 (C) 14 (D) 16 (E) 18 If the triangle is isosceles, 2 sides are have equal lengths We know that the perimeter of the triangle is 18, 2x + y = 18 where x is the length of the 2 sides with equal lengths and y is the length of the other side Now, we know that one of the sides is 8 There are two possibilities, when x = 8 or y =8 If x = 8, the three sides are 8,8,2 which is not possible(does not obey the properties of triangles) If y = 8, the three sides are 5,5,8 The area is \(2*\frac{1}{2}*4*3\) as it will form 2 right triangles with sides 3,4,5 Therefore, the area must be 12(Option B)8,8, and 2 is a possible isosceles triangle of area ~8. 88=0 <2 , 82= 6 <8 , 8+8= 16> 2, 8+2=10>8. it follows all required rules
Originally posted by rahulkashyap on 01 Sep 2017, 01:44.
Last edited by rahulkashyap on 01 Sep 2017, 01:50, edited 1 time in total.



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Re: Which of the following could be the area of an isosceles triangle with
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01 Sep 2017, 01:49
Makesh617 wrote: pushpitkc wrote: Bunuel wrote: Which of the following could be the area of an isosceles triangle with perimeter 18 and one side of length 8?
(A) 6 (B) 12 (C) 14 (D) 16 (E) 18 If the triangle is isosceles, 2 sides are have equal lengths We know that the perimeter of the triangle is 18, 2x + y = 18 where x is the length of the 2 sides with equal lengths and y is the length of the other side Now, we know that one of the sides is 8 There are two possibilities, when x = 8 or y =8 If x = 8, the three sides are 8,8,2 which is not possible(does not obey the properties of triangles) If y = 8, the three sides are 5,5,8 The area is \(2*\frac{1}{2}*4*3\) as it will form 2 right triangles with sides 3,4,5 Therefore, the area must be 12(Option B)Can u explain y 8,8,2 is not a valid triangle Sent from my A0001 using GMAT Club Forum mobile appHi Makesh617, My apologies, made the correction. The area of a triangle with sides 8,8,2 is less than 8 and that is not an answer option
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Re: Which of the following could be the area of an isosceles triangle with
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07 Sep 2017, 07:13
Bunuel wrote: Which of the following could be the area of an isosceles triangle with perimeter 18 and one side of length 8?
(A) 6 (B) 12 (C) 14 (D) 16 (E) 18 Since the isosceles triangle has a perimeter of 18 and a side length of 8, we could have the following sides: 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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