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3 years ago

Will a 11.5-inch x 18-inch rectangular tray fit in the box shown? Explain.

Mathematics

1 answer:

pychu [463]3 years ago

3 0

Answer:

Option D

Step-by-step explanation:

From the picture attached,

In the parallelogram ABCD,

Length of diagonals AC and BD are equal.

By the property,

"If the lengths of the diagonals of a parallelogram are equal, parallelogram will be a rectangle".

Therefore ABCD is a rectangle.

That means all interior angles of the given rectangle will be 90°.

Now we apply Pythagoras theorem in right triangle ΔABC,

AC² = AB² + BC²

(22)² = (12)² + (BC)²

484 - 144 = (BC)²

BC = √340

BC = 18.44 inches

Dimensions of the given box are 12 inches by 18.44 inches.

Dimensions of the rectangular tray is 11.5 inches by 18 inches.

Since, dimensions of the box are larger than the dimensions of the tray, tray can be adjusted in the box.

Therefore, Option D will be the answer.

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