Question

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The lengths of the sides of an isoceles trapezoid are 10,10,13, and 19. Compute the length of one diagonal of the isoceles trapezoid. Express your answer in simplified radical form.

Answer 1

d = √347

Explanation:

You can use Pythagoras' theorem twice to determine the length of the diagonal.

Consider the isosceles trapezoid PQRS in the diagram below.

ST = ½(19 - 13) = ½ × 6 = 3

∆PST is a right triangle

∴ PT² + 3² = 10²

PT² = 10² - 3² = 100 - 9 = 91

∆PRT is a right triangle.

∴ PR² = RT² + PT²

PR² = 16² + 91 = 256 + 91 = 347

PR = √347

The length of the diagonal is √347