Question

Sasha ordered a kite online. When it arrived, the kite was missing the crossbar. What length crossbar does Sasha need to complete the kite? Round to the nearest tenths if necessary.

Answer 1

Approximately
`5.7` inches

Explanation:

The crossbar and two given lengths form a right triangle. We know this because we see a right angle marked on the diagram in between the two given sides.

In this case, we have a right triangle with legs of
`4` and
`4`, and we need to find the hypotenuse. By the Pythagorean Theorem (
`a^(2) +b^(2) =c^(2)`, where
`a` and
`b` are the legs and
`c` is the hypotenuse), we get:

`4^(2) +4^(2) =c^(2)`

`16+16=c^(2)` (Evaluate exponents)

`32=c^(2)` (Combine like terms)

`√(32)=\sqrt{c^(2)}` (Take the square root of both sides of the equation to get rid of
`c`'s exponent)

`c=4√(2) ,c=-4√(2)`

The latter solution is an extraneous solution because the side lengths of a triangle cannot be negative. Therefore, the answer is
`4√(2) \approx 5.7` inches. Hope this helps!