Question

A carpenter measured the dimensions of the floor in a rectangular room. He rounded the measurements to the
nearest foot and recorded them as shown.

width = 9 feet
length = 15 feet

Based on the rounded measurements, which of the following statements could be true?

A) The actual width of the floor is 8 feet 4 inches,

B) The actual length of the floor is 15 feet 5 inches.

C) The actual area of the floor is 149.5 square feet.

D) The actual perimeter of the floor is 44 feet 10 inches.

Answer 1

B because is the closest to 9 feet wide and length of 15 feet

Answer 2

Assuming errors in the measures of the dimensions, we can see that the first two statements could be true.

Which of the given statements is true?

We have a rectangular room, such that its dimensions (rounded) are:

• width = 9ft
• length = 15ft

So the width can be any value in the range:

W ∈ (8.5ft, 9.4ft)

And the length:

L  ∈ (14.5ft, 15.4ft)

Now, i we use the two maximum values for L and W, the maximum area that we get:

$W*L = 9.4ft*15.4ft = 144.76 ft^2$

So the third statement can be discarded.

And the minimum perimeter is:

P = 2*(8.5ft + 14.5ft) = 46ft

So we also can discard the last option.

Then, the only two options that could be true (assuming errors in the measurement or error in the tool used) the first two statements could be true.

If you want to learn more about measures:

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