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

**Problem**

**Problem**

What is the length of the diagonal in the parallelepiped with dimensions 11, 8 and 6 units of length.

- 13.5 units
- 14.8 units
- 10.3 units
- 19.5 units
- 25.3 units

**The Usual Method**

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The length of the diagonal of the parallelepiped is given by:

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**(Ans: 2)**

*Estimated Time to arrive at the answer = 45 seconds because of taking a square root of a non perfect square number.*

**Using Technique**

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Using some fundamental concepts of geometry as shown below:

The diagonal cannot be larger than the sum of all the three sides: 11 + 8 + 6 = 25 < 25.3. This eliminates option ‘5’.

Find the pairs of sums of length of sides as follows: 11 + 8 =19, 11 + 6 = 17 and 8 + 6 = 14. The answer has to lie between the largest sum and the smallest sum. i.e. between 19 and 14. This leaves us only with option ‘2’ as the answer.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 10 seconds.*

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