The Diagonals of a Rectangle — Practice Geometry Questions

By Allen Ma, Amber Kuang

A rectangle is a parallelogram with four right angles, which allows you to apply the Pythagorean theorem when trying to find missing sides or angles. The following practice geometry questions ask you to find the diagonal and side length for two different rectangles.

Practice questions

Find the length of the diagonal of rectangle RSTW.

  1. In rectangle RSTW, SR = 5 and RW = 12. Find the length of

    image0.png

  2. In rectangle RSTW, the length of

    image1.png

    is 7 more than the length of

    image2.png

    and the length of

    image3.png

    is 8 more than the length of

    image4.png

    Find the length of

    image5.png

Answers and explanations

  1. 13

    A rectangle contains four right angles, and the diagonal of a rectangle creates a right triangle. This particular right triangle has legs measuring 5 and 12, with the diagonal being the hypotenuse. Use the Pythagorean theorem to solve for the hypotenuse:

    image6.png

  2. 13

    image7.png

    Let

    image8.png

    Opposite sides of a rectangle are congruent, which means that ST = x + 7 and that TW = x.

    A rectangle contains four right angles, and the diagonal of a rectangle creates a right triangle. This right triangle has legs measuring x and x + 7, with the hypotenusemeasuring x + 8. Use the Pythagorean theorem to solve for x:

    image9.png

    If x = 5, then RT = x + 8 = 5 + 8 = 13.

    image10.png

    are diagonals of the rectangle. Because the diagonals of a rectangle are congruent, SW = 13 as well.