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## OG 2020: Question No. 99

In the floor plan of an executive’s beach house above, the north and south walls of the living room are parallel. What is the floor area, in square feet, of the bedroom?

1. 450√3
2. 450
3. 225√3
4. 225
5. It cannot be determined from the information given.
 Source OG 2020 Type Problem Solving Topic Geometry Sub-Topic Triangle Difficulty Medium

### Solution

#### Given

Let us name the point in the diagram as shown below:

• AE = 30 ft
• BE = 30 ft
• CF = 15 ft
• CD = 30 ft

#### To Find:

• Area of Bedroom or ∆ACD

#### Approach and Working:

Since EF is parallel to BC, So, two corresponding angles of ∆AEF and ∆ABC will be equal.

• ∆AEF and ∆ABC are similar triangles.
• Therefore, AE/ AB = AF /FC
• 30/(30 + 30) = x/(x + 15)
• x = 15
• AC = x + 15 = 30 ft
• Hence, ∆ACD is an equilateral triangle since all the sides are equal.
• Thus, Area of ∆ACD = √3/4 * 302 = 225√3

Therefore, option C is the correct answer.

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