The length of the diagonal

Question

The width of a rectangle is 9 less than twice it’s length. If the area of the rectangle is 190 cm^2, what is the length of the diagonal?

Answer 1

For this type of question, we should find the value of the length and width of the rectangle, then use Pythagorean theorem to determine the diagonal.

Step 1: determine the length and width. Using the formula A = LW, we plug in A = 190 cm² and W = 2L -9. This gives us 190 = L(2L-9) as an equation we can use to find the length. Solved, it gives us 12.25 cm as the length. When we use the length to find the width, we get W = 2(12.25) - 9 = 15.5

Step 2: Use the Pythagorean theorem to determine the length of the diagonal, the length and width will be the opposite and adjacent and the diagonal will be our hypotenuse.

diagonal = sqrt((12.25)² + (15.5)²⁾ =19.76cm.

Answer 2