Quadratic Equations

Question

Use the Pythagorean Theorem and the square root property to solve the following problem. Express your answer in simplified radical form. Then find a decimal approximation to the nearest tenth.

A rectangular park is 21 miles long and 7 miles wide. How long is a pedestrian route that runs diagonally across the​ park?

In simplified radical​ form, the pedestrian route is how many miles long?

Answer 1

The diagonal (x) would be the hypotenuse of the right triangle and the length (21) and width (7) would be the legs.

By the Pythagorean theorem: 21^2 + 7^2 = x^2

x^2 = 490

x^2 = 49 * 10

x = 7 * sqrt(10)