Question

a custom aquarium is being designed to fit into a corner of the room creating a an isosceles right triangle. if one leg of the aquarium is 20 inches from the corner to the end of one doorway wall, what is the hypotenuse? round to the nearest tenth. enter your answer in the box.

Explanation:

Step1: Identify the legs' lengths

In an isosceles right - triangle, the two legs have equal lengths. Given one leg is 20 inches, so \(a = b=20\) inches.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse. Substitute \(a = 20\) and \(b = 20\) into the formula: \(c^{2}=20^{2}+20^{2}=400 + 400=800\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{800}\approx28.3\) inches.

Answer:

28.3 inches