Please Help! Geometry

Question

The hypotenuse of a right triangle is (Square root 8) as long as one of the legs. If the perimeter of the triangle is 35 cm, determine the length of the hypotenuse, accurate to three places after the decimal point.

Answer 1

Let a be the length of the one leg. The hypotenuse, c, is (√8)a. Let's label the other leg as b. Applying the Pythagorean Theorem:

a² + b² = c²

a² + b² = 8a²

b² = 8a² - a²

b² = 7a²

b = (√7)a

Now the perimeter:

a + b + c = 35 cm

a + (√7)a + (√8)a = 35 cm

Factor out the a:

a·(1 + √7 + √8) = 35

Use your calculator to compute the quantity in parentheses then solve for a. Once you have the value of a, the length of the hypotenuse is (√8)a. The units are cm.