An isosceles right triangle has legs that are each 4cm. What is the length of the hypotenuse?

2 Answers
Nov 14, 2015

Answer:

#c = sqrt(32)#

Explanation:

We will use the Pythagorean Theorem for this problem.

We know that each leg is #4cm#. We can plug those in for #a# and #b#, to find our hypotenuse, #c#.

#4^2 + 4^2 = c^2#
#16 + 16 = c^2#
#32 = c^2#
#c = sqrt(32)#

Nov 14, 2015

Answer:

#4sqrt(2)"cm"#

Explanation:

By the Pythagorean theorem, the square of the hypotenuse of a right triangle is equal to the sum of the squares of it's legs. That is, for a right triangle with legs #a# and #b# and hypotenuse #c#
#a^2 + b^2 = c^2#

In this case, we have #a = b = 4"cm"#, thus

#c^2 = (4"cm")^2 + (4"cm")^2 = 32"cm"^2#

#=> c = sqrt(32"cm"^2) = sqrt(16*2)"cm" = 4sqrt(2)"cm"#