Question

What is the length of AB, written in simplest radical form and what is the perimeter of the triangle?

Answer 1

Answer:

• AB = 3√3;
• P = 2√5 + 3√3 + √7.

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AB is the missing hypotenuse of the right triangle with shown legs.

Find AB using Pythagorean theorem:

• $AB=\sqrt{AC^2+BC^2}$

• $AB = \sqrt{(2\sqrt{5} )^2+(\sqrt{7})^2}=\sqrt{4*5+7}=\sqrt{27}=3\sqrt{3}$

Find the perimeter:

• P = AC + BC + AB
• P = 2√5 + 3√3 + √7