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Geometry Smart Math

[Smart Math] Geometry Problem 14

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

Geometry

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?

  1. 18 feet
  2. 19 feet
  3. 20 feet
  4. 21 feet
  5. 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:

\frac{x}{24}=\frac{3}{4}

\therefore x=\frac{3\times 24}{4}= 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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