How to Calculate the Width of a Rectangle Using the Diagonal

Measuring right triangles to calculate width

To calculate the width of a rectangle using the diagonal you need to use the Pythagorean Theorem. The diagonal will cut the rectangle into two triangles. The Pythagorean Theorem is the formula "A" squared plus "B" squared equals "C" squared. "A" represents the height; "B" represents the width; and "C" represents the diagonal. To determine the width using this theory with a diagonal, you need to measure the height of the triangle you create using the diagonal.

Things You'll Need

• Ruler or Tape Measure

Instructions

1. Measure the height of the diagonal from the highest part of the triangle straight down to the bottom of the triangle. For example, measure the tallest part of a right triangle to the ground, and the height measures 2 feet.

2. Write out the formula, "C" squared divided by "B" squared equals "A" squared. Replace "C" with the diagonal and "B" with the height. For example, the diagonal is 5 feet and the height is 2 feet. So 5 squared divided by 2 squared equals the width squared.

3. Solve the problem. In the example, 5 squared is 25; and 2 squared is 4. So, 25 divided by 4 equals 6.25. This number is the square of the width, so you need the square root of the amount to calculate the width. In the example, the square root of 6.25 is 2.5. So the width of the triangle is 2.5 feet.

References

• Pythagorean Theorem Proof