Question

A textbook has a length of 6 inches, a height of y inches, and a width of x inches. If the length of the diagonal of the front cover is 8 inches and the length of the diagonal of the width is 7 inches, find the values of x and y.

Answer 1

x = 2√7, y = √21

Explanation:

The textbook has right angles, so we can use Pythagorean theorem to find the missing lengths.

For the triangle on top of the textbook:

c² = a² + b²

8² = 6² + x²

64 = 36 + x²

28 = x²

x = √28

x = 2√7

For the triangle on the side of the textbook:

c² = a² + b²

7² = x² + y²

49 = 28 + y²

21 = y²

y = √21