Question

The diagonal length of a rectangle is 21 inches, and the length of the rectangle is 8 inches. Which measurement is closest to the width of this rectangle in inches? 13 in. 19. 4 in. 22. 5 in. 29 in.

Answer 1

The diagonal of the rectangle cut the rectangle in the shape of right angle with length of hypotenuse equal to the length of diagonal.

The measure of the width of the rectangle is 22.5 inches (approx.) The option 3 is the correct option.

What is the diagonal of the rectangle?

The diagonal of a rectangle cuts the rectangle into the two equal right angles. In this the length hypotenuse of the right angle is equal to the measure of the diagonal of the rectangle.

Given information-

The diagonal length of a rectangle is 21 inches.

The length of the rectangle is 8 inches.

As the diagonal of the rectangle cut the rectangle in the shape of right angle with length of hypotenuse equal to the length of diagonal as shown in figure.

Suppose the width of the rectangle is $x$ meter long. Thus according to the Pythagoras theorem,

$x^2+8^2=21^2\\x^2+64=441\\x^2=441-64\\x=\sqrt{505}\\ x=22.472$

Hence the measure of the width of the rectangle is 22.5 inches (approx.) The option 3 is the correct option.

Learn more about the diagonal of rectangle here;

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