Question

The length of rectangular painting is 7 inches long than its width. If the diagonal is 13inches, what are the dimensions of the painting?

Answer 1

Answer:

5 inches by 12 inches

Explanation:

Let the width of the painting be x.

Length of painting = x + 7

Diagonal = 13 inches

Using Pythagoras Theorem,

(Diagonal)² = (Length)² + (Width)²

=> (13)² = (x + 7)² + (x)²

=> 169 = x² + 14x + 49 + x²

=> 169 - 49 = 2x² + 14x

=> 120 = 2x² + 14x

=> 120 = 2 (x² + 7x)

=> 60 = x² + 7x

=> x² + 7x - 60 = 0

=> x² - 5x + 12x - 60 = 0

=> x (x - 5) + 12 (x - 5) = 0

=> x = 5

Hence, the dimensions are 5 inches by 12 inches.