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

**Problem**

**Problem**

The area of the four walls of a room is 1080 sq.ft. If the height and length of the room are in the ratio of 2 : 5 and the height and breadth are in the ratio 4 : 5. What is the area of the roof?

- 240 sq.ft.
- 450 sq.ft.
- 540 sq.ft.
- 720 sq.ft.
- Cannot be determined

**The Usual Method**

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Let the height and breadth of the room be 2*x* and 5*x* respectively.

Similarly let the height and breadth of the room be 4*y* and 5*y* respectively.

Area of the walls = length x height x 2 + breadth x height x 2 = 1080

……Eq. 1

Also note that height of the room is constant, so:

Substituting this in Eq. 1, we get:

Hence, length of room = ft

And breadth of room = ft

Hence area of roof = 30 x 15 = 450 sq.ft.

**(Ans: 2)**

*Estimated Time to arrive at the answer = 90 seconds.*

**Using Technique**

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Ratio of height to length = 2 : 5 = 4 : 10

Ratio of height to breadth = 4 : 5

Thus ratio of length to breadth = 10 : 5

Hence, area of ceiling =

Hence, the area of the ceiling should be a multiple of 50. The only option satisfying this condition is option ‘2’.

**(Ans: 2)**

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

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