A floor plan shows that the exterior of a room has dimensions 12 feet by 17 feet. If the area of the room measured from the interior is only 176 square feet, express the thickness of the surrounding walls in feet. (Assume that the walls have uniform thickness).

Question

Mathematics

Ronan Osborne

20 September, 18:06

A floor plan shows that the exterior of a room has dimensions 12 feet by 17 feet. If the area of the room measured from the interior is only 176 square feet, express the thickness of the surrounding walls in feet. (Assume that the walls have uniform thickness).

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Answers (1)

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Camryn Garner · Answer 1

The thickness of the walls is 0.5 feet.

Step-by-step explanation:

Let's call the thickness of each all by T.

The external dimensions of the room are 12 feet by 17 feet, and these values include thickness of 2 walls each, so the internal dimensions are (12-2T) and (17-2T).

If the internal area is 176, we have the equation:

(12-2T) * (17-2T) = 176

204 - 58T + 4T2 = 176

4T2 - 58T + 28 = 0

2T2 - 29T + 14 = 0

Using Bhaskara, we have:

Delta = (-29) ^2 - 4*2*14 = 729

sqrt (D) = 27

T1 = (29 + 27) / 4 = 14 feet

T2 = (29 - 27) / 4 = 0.5 feet

As the first value is too big and would generate a negative side for the room, we have that the thickness of the walls is 0.5 feet.