Question

Here is the whole floor that Zahra's office is on.Each room is a scaled copy of every other room. the scale for this blueprint 6 cm to 15 ft. Determine the actual area of the room with question mark​

Answer 1

`Area = 1,012.5\ ft^2`

Explanation:

Zahra's office is made of several rooms each one of which is a scaled copy of the others.

We have the complete dimensions of one of them and it's evident that the lengths of the rooms are twice the width.

With this information, we'll find the area of the room with the question mark.

We have added some dimensions marked with additional variables.

The room with 8 cm of width has a length of y. Since all lengths are twice the widths, y=16 cm.

The room with 8 cm length has width z which is half of the length, z=4 cm.

The room with dimensions u and w has a length of y+z=20 cm. Thus w=20 cm. The width u is half of w, thus u=10 cm.

The length of the room with the question mark is x, and x = 8 cm + u = 18 cm

The width of that room is half of x, v=9 cm.

The area is 9 * 18 = 162
`cm^2`

Since the scale of the blueprint is 6 cm to 15 ft, the actual area of the room is:

`\displaystyle Area = 162\ cm^2 * \left((15\ ft)/(6\ cm)\right)^2`

`Area = 1,012.5\ ft^2`