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

Answer 1

#4sqrt(2)"cm"#

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"#

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Answer 2

Sadie Allen

#c = sqrt(32)#

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)#

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Answer 3

Ella Armstrong

The length of the hypotenuse of an isosceles right triangle with legs of length 4 cm each is (4\sqrt{2}) cm.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.