Question

A landscaper wants to put a square reflecting pool next to a triangular deck, as shown below. The triangular deck is a right triangle, with legs of length 9 feet and 11 feet, and the pool will be adjacent to the hypotenuse. (a) Use the Pythagorean Theorem to find the length of a side of the pool. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the pool.

Name: Problem 310, Chapter 9: Elementary Algebra
Uploaded: 2021-07-27T05:31:22-08:00
Duration: 5 min 20 s
Channel: Gokul R Nair
Description: A landscaper wants to put a square reflecting pool next to a triangular deck, as shown below. The triangular deck is a right triangle, with legs of length 9 feet and 11 feet, and the pool will be adjacent to the hypotenuse. (a) Use the Pythagorean Theorem to find the length of a side of the pool. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the pool.

   A landscaper wants to put a square reflecting pool next to a triangular deck, as shown below. The triangular deck is a right triangle, with legs of length 9 feet and 11 feet, and the pool will be adjacent to the hypotenuse.
(a) Use the Pythagorean Theorem to find the length of a side of the pool. Round your answer to the nearest tenth of a foot.
(b) Find the exact area of the pool.

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 9, Problem 310

Instant Answer

Solved by Expert Gokul R Nair

07/27/2021

Step 1

The hypotenuse of this triangle is the side of the square pool. We can use the Pythagorean theorem to find the length of the hypotenuse. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the Show more…

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A landscaper wants to put a square reflecting pool next to a triangular deck, as shown below. The triangular deck is a right triangle, with legs of length 9 feet and 11 feet, and the pool will be adjacent to the hypotenuse. (a) Use the Pythagorean Theorem to find the length of a side of the pool. Round your answer to the nearest tenth of a foot. (b) Find the exact area of the pool.

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Key Concepts

Area of a Square

The area of a square is calculated by squaring the length of one of its sides. This formula is essential in finding the extent of the space enclosed within the borders of a square, and it demonstrates how linear dimensions translate into two-dimensional measures.

Pythagorean Theorem

This principle states that in a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. It is a fundamental concept in Euclidean geometry used to determine the missing side length of a right triangle when the other two sides are known.

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