Question

the isosceles right triangle shown above has a hypotenuse of 20√2 centimeters. what is the perimeter, in centimeters, of the triangle? a 40√2 b 40 + 20√2 c 60√2 d 20 + 40√2 e 40 + 40√2

Explanation:

Step1: Use the property of isosceles right - triangle

In an isosceles right - triangle, if the length of the hypotenuse is \(c\) and the length of each of the equal sides is \(a\), then \(c = a\sqrt{2}\). Given \(c=20\sqrt{2}\), we can solve for \(a\).
From \(c = a\sqrt{2}\), substituting \(c = 20\sqrt{2}\), we get \(20\sqrt{2}=a\sqrt{2}\). Dividing both sides by \(\sqrt{2}\), we find \(a = 20\).

Step2: Calculate the perimeter

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. For an isosceles right - triangle with sides \(a\), \(a\), and \(c\), \(P=a + a + c\).
Substituting \(a = 20\) and \(c=20\sqrt{2}\), we have \(P=20 + 20+20\sqrt{2}\).
Simplifying, \(P = 40+20\sqrt{2}\).

Answer:

B. \(40 + 20\sqrt{2}\)