Question

The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 21 cm, what is the length of the diagonal? Note: Your answer must be a number. It may not contain any arithmetic operations. The length of the diagonal is cm.

Answer 1

Step 1: Set length = x

Step2: Width = 2x-7

Step 3: Area = 145 cm^2 = length * width = x(2x-7)

Step 4: 2(x^2)-7x = 145 cm^2

Step 5: 2(x^2)-7x-145=0

Step 6: Use quadratic equation to solve for x

Step 7: x=10.44266932535685 cm

Step 8: Set diagonal = d

Step 9: Use Pythagorean theorem to find the diagonal

Step 10: d = 17.373887650257 cm

Therefore the length of the diagonal is about 17.4 centimeters.

Note: Rounding or estimating would make this problem look alot easier but the question didn't specify that so you can go with the long decimal answer or the simple and short rounded answer depending on your case.