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

**Problem**

**Problem**

Find the distance between points P (-3, 2) and Q (-5, 8).

- units
- 4 units
- 6 units
- units
- units

**The Usual Method**

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Using formula of distance between two points =

=

=

= units

** **

**(Ans: 1)**

*Estimated Time to arrive at the answer = 30 seconds.*

**Using Technique**

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Difference between and = 2 units

Difference between and = 6 units

Since, the lines PQ, and form a right angled triangle with PQ as the hypotenuse. We already know that the hypotenuse of any right triangle should be more than the longest right side but less than the sum of the right sides. Thus length of PQ should be lying between 6 < PQ < (6 + 2). The only value satisfying this range is 6.3 units.

**(Ans: 1)**

*Estimated Time to arrive at the answer = 15 seconds.*

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