Find the nearest tenth of a foot

Question

An oriental rug is 3 feet longer than it is wide. If the diagonal of the rug is 12 feet,find the dimensions to the nearest tenth of a foot

Answer 1

If w represents the width, then w+4 represents the length. By the Pythagorean Theorem:

12² = w² + (w + 4)²

144 = w² + w² + 8w + 16

0 = 2w² + 8w - 128 = w² + 4w - 64 We can now use the quadratic formula:

w = (-4 +/- √(16 - (4 * - 64)))/2 = -2 +/- (√(16 - (-256)))/2 = -2 +/- (√272)/2 ≅ -2 +/- 8.3

Since we can't have a negative width, the dimensions are approximately 6.3 by 10.3