Question

Help ASAP! 20 Points!

Hilda looks at the blueprint plan of a four-walled room in which the walls meet each other at right angles. The length of one wall in the plan is 12 inches. The length of the diagonal of the floor of the room in the plan is approximately 16.97 inches.

Is the room in the shape of a square? Explain how you determined your answer. Show all your work.

Answer 1

Yes.

Explanation:

To determine if the room is a square, we can use the Pythagorean theorem. (For my example, we will be rounding 16.97 up to 17)

a² + b² = c²

Since we know that one wall is 12 inches, we can input 12 in the place of a.

(12)² + b² = c²

The diagonal of the room would be our hypotenuse meaning we can put 17 in the place of c.

(12)² + b² = (17)²

From here, solve for b. Your work should look similar to the following:

(12)² + b² = (17)²

144 + b² = (17)²

144 + b² = 289

b² = 145

√b² = √145

b = 12.04 (rounding)

b = 12

Since we have determined that b = 12 and we know that a = 12, this room is in the shape of a square.

~Hope this helps!~