Tim T. answered • 04/23/20

Math: K-12th grade to Advanced Calc, Ring Theory, Cryptography

Greetings! Lets solve this shall we ?

So, we must find out what the length of the diagonal within the rectangle given the length is l = x and the width is w = 2x - 2 with the Area of 183 square centimeters. Then, we yield the area of a triangle such that

A = l*w

183 = (x)(2x-2)...........Then distribute the x insides such that

183 = 2x^{2} - 2x...........Then we subtract 183 from both sides to get

2x^{2} - 2x - 183 = 0.......Since this is not factorable using a factoring method like the AC-method, we must use the Quadratic Formula such that a = 2, b = -2 and c = -183 to obtain

x = [2 +- √(1468)] / 4 = (2+38.31) / 4 = 10.1 centimeters. Then, we plug this into the width equation to get

width = 2(10.1) - 2 = 18.2 centimeters. Since the width is longer than the length, the length is really 18.2 centimeters and the width is 10.1 centimeters.

The rectangle makes 90 degree angles all the way around so we use Pythagorean to find the length of the diagonal such that

**diagonal = √[(10.1)**^{2}** + (18.2)**^{2}**] = 20.81 centimeters **(rounded to the nearest hundredth)

I hope this helped!