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Q. Find the perimeter of the isosceles triangle whose un

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Q. Find the perimeter of the isosceles triangle whose un  [#permalink]

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Q. Find the perimeter of the isosceles triangle whose unequal side is equal to 16 units and the area of the triangle is 48 sq.units

    A. 24 units
    B. 30 units
    C. 36 units
    D. 40 units
    E. 48 units


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Originally posted by EgmatQuantExpert on 27 Apr 2017, 00:11.
Last edited by EgmatQuantExpert on 07 Aug 2018, 05:04, edited 1 time in total.
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Re: Q. Find the perimeter of the isosceles triangle whose un  [#permalink]

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New post 27 Apr 2017, 00:11
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Re: Q. Find the perimeter of the isosceles triangle whose un  [#permalink]

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New post 27 Apr 2017, 01:17
EgmatQuantExpert wrote:
Q. Find the perimeter of the isosceles triangle whose unequal side is equal to 16 units and the area of the triangle is 48 sq.units

    A. 24 units
    B. 30 units
    C. 36 units
    D. 40 units
    E. 48 units


Thanks,
Saquib
Quant Expert
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Re: Q. Find the perimeter of the isosceles triangle whose un  [#permalink]

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New post 28 Apr 2017, 09:59
EgmatQuantExpert wrote:
Q. Find the perimeter of the isosceles triangle whose unequal side is equal to 16 units and the area of the triangle is 48 sq.units

    A. 24 units
    B. 30 units
    C. 36 units
    D. 40 units
    E. 48 units


Thanks,
Saquib
Quant Expert
e-GMAT


Great question. It tests a few key concepts simultaneously.

1. Properties of isosceles triangles: among others, if the median is drawn to the base (BM in diagram below):

a) the median is the altitude, which we need because we are given area and need to find perimeter, which will rely on property (1-c) below
b) the median/altitude is the perpendicular bisector of the base
c) it produces two congruent right triangles

Diagram is below

2. Draw a triangle ABC with base 16, other two equal sides labeled X. AB=BC

3. Draw the median, BM. Its height is derived from given area. Triangle area = 1/2*b*(height) => 48 = (1/2)(16)(BM) => 96 = 16 * BM => Height/BM = 6

4. Base AC is bisected perpendicularly, so we have two triangles with 90-degree angles and congruent sides, per c above. \(\frac{AC}{2}\) = \(\frac{16}{2}\)=8, 8=AM=CM. We now have two right triangles with values for legs: BM is 6, AM is 8 (CM also = 8).

5. Properties of right triangles: if you have two legs in the ratio 3x:4x, the hypotenuse will be 5x. (3-4-5 right triangle.) And per (a) and (c) above=>

6. Each equal side of the isosceles triangles is the hypotenuse of a 3-4-5 right triangle. You can either do the math with Pythagorean theorem or remember that 3-4-5 has all kinds of variations, including 6-8-10. We have BM is 6, AM is 8. So hypotenuse is 10.

Now you have two hypotenuse/equal sides of isosceles triangle with value X = 10. Find perimeter. 10 + 10 + 16 = 36.
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isosceles triangle.jpg
isosceles triangle.jpg [ 9.54 KiB | Viewed 4673 times ]


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Re: Q. Find the perimeter of the isosceles triangle whose un  [#permalink]

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New post 10 Oct 2018, 03:12
EgmatQuantExpert wrote:
Reserving this space to post the official solution. :)


Dear EgmatQuantExpert,

When you reserve space for a solution please kindly provide the solution afterwards, why else have you reserved the space for? I see many such question of yours , where your reserved space has remained unused . Kindly look into such questions and fulfill the purpose of your reservation. Hope you will see merit in this and do the needful. Thank you.
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Re: Q. Find the perimeter of the isosceles triangle whose un   [#permalink] 10 Oct 2018, 03:12
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