[Smart Math] Geometry Problem 13

Here’s and example of a SMART MATH problem for GEOMETRY.

Problem

The equal sides of an isosceles triangle are even integers only. What is the area of the triangle if the perimeter is 7 units?

1. 7 sq. units
2. 3 sq. units
3. 8 sq. units
4. sq. units
5. sq. units

The Usual Method

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Even integers are 2, 4, 6 … Now to have the perimeter as 7 i.e. a + a + b = 7, where ‘1’ is the length of equal side and is an even integer.

Hence, 2a + b = 7

Now a can take the value of 2 only.

So 2(2) + b = 7

b = 3

Hence dimension of the triangle = 2, 2, and 3 units.

Hence, area of this triangle using semi-perimeter formula (Area = , where = semi-perimeter)
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In this case, s =
<br />
Area =
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=
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= sq. units

(Ans: 4)

Estimated Time to arrive at the answer = 45 seconds.

Using Technique

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Once you reach to a the level of identifying the dimensions of the triangle (2, 2 and 3), put the values as , to get the answer.

Now, do not solve this. Just by observing it, you will see that there are four 2s in the denominator with the sign. Hence, the denominator will be = 4. Also 7 is a prime number so … will have (or one of its form) as the numerator. Hence the answer should have . This format is only in option ‘4’.

(Ans: 4)

Estimated Time to arrive at the answer = 15 seconds.
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