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

**Problem**

**Problem**

A certain pole casts a shadow 24 feet long. At the same time another 3 feet high casts a shadow 4 feet long. How high is the first pole given that the heights and shadows are in proportion?

- 18 feet
- 19 feet
- 20 feet
- 21 feet
- 22 feet

**The Usual Method**

Let the height of the pole whose shadow is 24 feet long be ‘*x*’ feet high.

Since both the length of the poles and its shadow are in proportion, than:

18 feet

**(Ans: 1)**

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

**Using Technique**

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Since height of pole and its shadow are in proportion, we notice that for a pole of 3 feet height, the shadow is 4 feet long. Thus by reducing ¼th (25%) of the length of the shadow, we can get the length of the pole. Thus by doing a 25% reduction on the length of 24 feet long shadow, we can get the height of the pole that casts this shadow.

25% reduction on 24 feet is 24 – 6 = 18 feet.

**(Ans: 1)**

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

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