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# [Smart Math] Geometry Problem 8

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

### Problem

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

1. 13.5 units
2. 14.8 units
3. 10.3 units
4. 19.5 units
5. 25.3 units

### The Usual Method

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

$\sqrt{11^{2}+8^{2}+6^{2}}$

$=\sqrt{121+64+36}=\sqrt{321}\approx 14.8$

(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

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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