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The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet. Which measurement is closest to the length of this rectangle in feet?

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Answer: 12.4 feet

Step-by-step explanation:

This is the application of Pythagoras theorem.

The diagonal of the rectangle is the hypotenuse , to find the length , we will apply Pythagoras theorem , which states that :

the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.That is

[tex]hypotenuse^{2}[/tex] = [tex]opposite^{2} + Adjacent^{2}[/tex]

Let the length of the rectangle be [tex]x[/tex] , so we have :

[tex]13^{2}=x^{2} + 4^{2}[/tex]

which means that

[tex]x^{2} = 13^{2} - 4^{2}[/tex]

[tex]x^{2} = 169 - 16[/tex]

[tex]x^{2} = 153[/tex]

[tex]x = 12.369[/tex]

[tex]x[/tex] ≈ 12.4 feet

The length of the rectangle is 12.36 feet and this can be determined by using the Pythagorean theorem.

Given :

The width of a rectangle is 4 feet, and the diagonal length of the rectangle is 13 feet.

The following steps can be used in order to determine the length of the rectangle in feet:

Step 1 - The Pythagorean theorem can be used in order to determine the length of the rectangle in feet.

Step 2 - The mathematical expression of the Pythagorean theorem is given by:

[tex]\rm H^2 = P^2+B^2[/tex]   --- (1)

where H is the hypotenuse, B is the base, and P is the perpendicular.

Step 3 - According to the given data, the value of P is 4 feet and the value of H is 13 feet.

Step 4 - Substitute the known terms in the expression (1) in order to determine the length.

[tex]\rm 13^2 = 4^2+L^2[/tex]

[tex]\rm L^2 = 169-16[/tex]

L = 12.36 feet

For more information, refer to the link given below:

https://brainly.com/question/24252852

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