Question

skillstream: determining the distance between two points using the pythagorean theorem: 20 coins

type the answer in the space provided. use numbers instead of words.

christy builds a rectangular island in her kitchen. she uses one large marble slab for the islands countertop. the slab is 2.8 feet wide and 4.7 feet long. what is the distance between opposite corners of the countertop? round your answer to the nearest tenth.
answer

Explanation:

Step1: Identify the sides of the right - triangle

The width and length of the rectangular countertop form the two legs of a right - triangle. Let $a = 2.8$ feet and $b=4.7$ feet.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse (the distance between the opposite corners). So $c=\sqrt{a^{2}+b^{2}}=\sqrt{2.8^{2}+4.7^{2}}$.
First, calculate $2.8^{2}=2.8\times2.8 = 7.84$ and $4.7^{2}=4.7\times4.7 = 22.09$.
Then $a^{2}+b^{2}=7.84 + 22.09=29.93$.
So $c=\sqrt{29.93}\approx5.47$.

Step3: Round the answer

Rounding $5.47$ to the nearest tenth gives $5.5$.

Answer:

$5.5$