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-GMATGreat 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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90% (01:56) correct 
