Chapter 3: Q. 406 (page 408)

Seong is building shelving in his garage. The shelves are $36$ inches wide and $15$ inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

Short Answer

Expert verified

The brace should be $39$ inches long.

Step by step solution

Step 1. Given Information

Given that the shelves are $36$ inches wide and $15$ inches tall. He wants to put a diagonal brace across the back to stabilize the shelves.

The objective is to know how long should the brace be.

Step 2. Concept Used

The Pythagorean Theorem states that in any right triangle, $a^{2} + b^{2} = c^{2}$ where c is the length of the hypotenuse anda andb are the lengths of the legs.

Step 3. Find the length of the hypotenuse

As in the triangle the length of the two legs are $36$ and $15$ , so in the equation $a^{2} + b^{2} = c^{2}$ substitute $36$ for $a$ and $15$ for role="math" $b$ .

$\begin{array}{rcl} 36^{2} + 15^{2} & = & c^{2} \\ 1296 + 225 & = & c^{2} \\ 1521 & = & c^{2} \end{array}$

Taking square root both sides we get

$\begin{array}{rcl} \sqrt{1521} & = & \sqrt{c^{2}} \\ 39 & = & c \end{array}$

So, the brace should be $39$ inches long.

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Seong is building shelving in his garage. The shelves are $36$ inches wide and $15$ inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept Used

Step 3. Find the length of the hypotenuse

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Most popular questions from this chapter

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Seong is building shelving in his garage. The shelves are 36inches wide and 15inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept Used

Step 3. Find the length of the hypotenuse

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Logic and Functions

Geometry

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Seong is building shelving in his garage. The shelves are $36$ inches wide and $15$ inches tall. He wants to put a diagonal brace across the back to stabilize the shelves, as shown. How long should the brace be?