GMAT Questions | Geometry #2

This GMAT quant practice question is a problem solving question in Geometry. Concept: Area of an Isosceles triangle. It also tests the foundation concepts of Triangles and Heron's Formula.

Question 2: What is the area of an isosceles triangle if two of its sides measure 6 and 12?

1. 8 √5
2. 15 √5
3. 9 √15
4. 9 √5
5. 12 √5

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Video Explanation

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Explanatory Answer | GMAT Geometry

Step 1 of solving this GMAT Geometry Question: Possible values of the third side

The given triangle is an Isosceles triangle and hence, two of the three sides of the triangle are equal.
Hence, the third side of the triangle can either be 6 or be 12.

If the two equal sides of the triangle measure 6, the sides of the triangle become 6, 6, and 12.
However, the sum of the two smaller sides is not greater than the third side.
∴ 6 is not a possible value of the third side.

If the two equal sides of the triangle measure 12, the sides of the triangle become 6, 12, and 12.
The sum of the smaller two sides is greater than the third side, and hence, the value of the third side is 12.

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Step 2 of solving this GMAT Geometry Question: Compute Area of Triangle

If the three sides of the triangle are given, we can compute the area of the triangle by using Heron's formula.
By Heron's formula, the Area is given by A = \\sqrt{s(s-a)(s-b)(s-c)}),
where a, b, and c are the sides of the triangle and s is the semi-perimeter of the triangle.
s = \\frac{a + b + c}{2})
s = \\frac{6 + 12 + 12}{2}) → \\frac{30}{2}) → 15

Substituting the values of s, a, b, and c into Heron's formula,
A = \\sqrt{15(15-6)(15-12)(15-12)})
A = \\sqrt{15 * (9) * (3) * (3)})
A = 9 \\sqrt{15})

Choice C is the correct answer.