Question

Three picture frames were measured in inches and the results are shown below, without rounding. Determine which picture frame has a flawed construction because it does NOT have perpendicular side lengths based on the given measures.

A

B

C
HELP PLEASE NOWWWWW

Answer 1

In the case of the second frame, the sides are not perpendicular to each other.

Explanation:

A. The length (l) of the frame is 20 and width (w) is 15.

If the frame is a rectangular one, then diagonal (d) can be calculated from the Pythagoras Theorem as
`d^(2) = l^(2) + w^(2) = 20^(2) + 15^(2) = 625 = 25^(2)`

⇒ d = 25 (Also given)

So, the frame is rectangular one.

B. The length (l) of the frame is 22 and width (w) is 10.

If the frame is a rectangular one, then diagonal (d) can be calculated from the Pythagoras Theorem as
`d^(2) = l^(2) + w^(2) = 22^(2) + 10^(2) = 584`

⇒ d = 24.166 ≠ 24 (24 is the given value)

So, the frame is not a rectangular one.

C. The length (l) of the frame is 21 and width (w) is 20.

If the frame is a rectangular one, then diagonal (d) can be calculated from the Pythagoras Theorem as
`d^(2) = l^(2) + w^(2) = 21^(2) + 20^(2) = 841 = 29^(2)`

⇒ d = 29 (Also given)

So, the frame is rectangular one.

Therefore, in the case of the second frame, the sides are not perpendicular to each other. (Answer)