QuestionFind the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use $d = \sqrt{24^2 + 18^2}$ .

Studdy Solution

STEP 1

Assumptions1. The computer monitor is rectangular in shape. The length of the monitor is24 inches3. The height of the monitor is18 inches4. We are asked to find the length of the diagonal to the nearest inch5. We will use the Pythagorean theorem to solve this problem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

STEP 2

The Pythagorean theorem is given by $c^2 = a^2 + b^2$ where c is the length of the hypotenuse (in this case, the diagonal of the monitor), and a and b are the lengths of the other two sides (in this case, the length and height of the monitor).

STEP 3

Substitute the given values into the Pythagorean theorem.
$c^2 =24^2 +18^2$

STEP 4

Calculate the squares of24 and18.
$c^2 =576 +324$

STEP 5

Add the two values together.
$c^2 =900$

STEP 6

To find the length of the diagonal (c), we need to take the square root of both sides of the equation.
$c = \sqrt{900}$

STEP 7

Calculate the square root of900.
$c =30$ The length of the diagonal of the computer monitor is30 inches to the nearest inch.

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QuestionFind the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use $d = \sqrt{24^2 + 18^2}$ .

Studdy Solution

STEP 1

STEP 2

The Pythagorean theorem is given by $c^2 = a^2 + b^2$ where c is the length of the hypotenuse (in this case, the diagonal of the monitor), and a and b are the lengths of the other two sides (in this case, the length and height of the monitor).

STEP 3

Substitute the given values into the Pythagorean theorem.
$c^2 =24^2 +18^2$

STEP 4

Calculate the squares of24 and18.
$c^2 =576 +324$

STEP 5

Add the two values together.
$c^2 =900$

STEP 6

To find the length of the diagonal (c), we need to take the square root of both sides of the equation.
$c = \sqrt{900}$

STEP 7

Calculate the square root of900.
$c =30$ The length of the diagonal of the computer monitor is30 inches to the nearest inch.

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QuestionFind the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use d=242+182d = \sqrt{24^2 + 18^2}d=242+182​.

Studdy Solution

STEP 1

STEP 2

The Pythagorean theorem is given byc2=a2+b2c^2 = a^2 + b^2c2=a2+b2where c is the length of the hypotenuse (in this case, the diagonal of the monitor), and a and b are the lengths of the other two sides (in this case, the length and height of the monitor).

STEP 3

Substitute the given values into the Pythagorean theorem.c2=242+182c^2 =24^2 +18^2c2=242+182

STEP 4

Calculate the squares of24 and18.c2=576+324c^2 =576 +324c2=576+324

STEP 5

Add the two values together.c2=900c^2 =900c2=900

STEP 6

To find the length of the diagonal (c), we need to take the square root of both sides of the equation.c=900c = \sqrt{900}c=900​

STEP 7

Calculate the square root of900.c=30c =30c=30The length of the diagonal of the computer monitor is30 inches to the nearest inch.

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QuestionFind the diagonal length of a monitor with dimensions 24 inches (length) and 18 inches (height) to the nearest inch. Use $d = \sqrt{24^2 + 18^2}$ .

The Pythagorean theorem is given by $c^2 = a^2 + b^2$ where c is the length of the hypotenuse (in this case, the diagonal of the monitor), and a and b are the lengths of the other two sides (in this case, the length and height of the monitor).

Substitute the given values into the Pythagorean theorem.
$c^2 =24^2 +18^2$

Calculate the squares of24 and18.
$c^2 =576 +324$

Add the two values together.
$c^2 =900$

To find the length of the diagonal (c), we need to take the square root of both sides of the equation.
$c = \sqrt{900}$

Calculate the square root of900.
$c =30$ The length of the diagonal of the computer monitor is30 inches to the nearest inch.