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Lapatulllka [165]
2 years ago
15

A carpenter braces a 10-ft x 15-ft wall by nailing a board diagonally across the wall. How long is the bracing board? Write your

answer in simplest radical form and round the answer to the nearest tenth.
Mathematics
1 answer:
lana66690 [7]2 years ago
8 0

Answer:

Radical: 5√13

Decimal: 18.0

Step-by-step explanation:

Given the dimension of the board given as 10ft by 15ft

If the board is nailed diagonally, the length of the bracing board will be gotten using the pythagoras theorem;

d² = 10² + 15²

d² = 100 + 225

d² = 325

d = √325

Expressing in radical form;

d = √325

d = √25*13

d = 5√13

Hence the length of the board in radical form is 5√13 feet

Express in decimal form;

d = √325

d = 18.0

Hence the length of the board to the nearest tenth is 18.0 feet

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Given right triangle ABCABC with altitude \overline{BD}
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Answer:

x = 2\sqrt{11}

Step-by-step explanation:

AD = 4

AC = 11

DC = 11 - 4 = 7

First, find BD using the right triangle altitude theorem:

BD = \sqrt{AD*DC}

Plug in the values

BD = \sqrt{4*7}

BD = 2\sqrt{7}

Use pythagorean theorem to find x:

x² = AD² + BD²

Plug in the values

x^2 = 4^2 + (2\sqrt{7})^2

x^2 = 4^2 + (2\sqrt{7})^2

x^2 = 16 + (4*7)

x^2 = 16 + 28

x^2 = 44

Take the square root of both sides

\sqrt{x^2} = \sqrt{44}

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x = \sqrt{4 * 11}

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Answer:

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Answer:

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Step-by-step explanation:

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