Question

4 the figure on the right shows the floor plan of three square rooms. the entire floor area of each room will be covered with a carpet. which one of the following statements is true? (note: the figure is not drawn to scale.) a the combined size of the carpets needed for room 1 and room 2 is the same as the size of the carpet needed for room 3. b the size of the carpet needed for room 3 is thrice the size of the carpet needed for room 1. c the size of the carpet needed for room 3 is twice the size of the carpet needed for room 1. d the combined size of the carpets needed for room 1 and room 2 is twice the size of the carpet needed for room 3.

Explanation:

Step1: Identify the triangle type

The triangle between the three square rooms is a right - triangle (since there is a right - angle symbol). Let the side length of Room 1 be \(a\), so the area of Room 1, \(A_1=a^{2}\). Let the side length of Room 2 be \(b\), so the area of Room 2, \(A_2 = b^{2}\). Let the side length of Room 3 be \(c\), so the area of Room 3, \(A_3=c^{2}\).

Step2: Apply the Pythagorean theorem

For a right - triangle, by the Pythagorean theorem, \(a^{2}+b^{2}=c^{2}\). Since \(A_1 = a^{2}\), \(A_2=b^{2}\) and \(A_3 = c^{2}\), we can substitute these into the Pythagorean theorem. So \(A_1 + A_2=A_3\). This means that the combined size of the carpets needed for Room 1 and Room 2 (which is \(A_1 + A_2\)) is the same as the size of the carpet needed for Room 3 (which is \(A_3\)).

Answer:

A. The combined size of the carpets needed for Room 1 and Room 2 is the same as the size of the carpet needed for Room 3.