And I saucily‘s right triangles legs are 10 square root of 8 feet long. What is the length of the hypotenuse?

2 Answers
Feb 25, 2018

See a solution process below:

Explanation:

Because we are told the isosceles triangle is a right triangle we can use the Pythagorean Theorem to determine the length of the hypotenuse.

The Pythagorean Theorem states:

#c^2 = a^2 + b^2#

Where:

#a# and #b# are the length of the legs of the right triangle.

For this problem both legs have the same length: #10sqrt(8)#

#c# is the length of the hypotenuse. What we are solving for in this problem.

Substituting for #a# and #b# and solving for #c# gives:

#c^2 = (10sqrt(8))^2 + (10sqrt(8))^2#

#c^2 = (10^2(sqrt(8))^2) + (10^2(sqrt(8))^2)#

#c^2 = (100 xx 8) + (100 xx 8)#

#c^2 = 800 + 800#

#c^2 = 1600#

#sqrt(c^2) = sqrt(1600)#

#c = 40#

The length of the hypotenuse is 40 feet.

Feb 25, 2018

The hypotenuse is #"40 ft"# long.

Explanation:

Right Isosceles Triangle

https://commons.wikimedia.org/wik

The ratio of the sides in an Isosceles right triangle is #1:1:sqrt2#.

This tells us that the two sides, apart from the hypotenuse, will always be the same length.

We are given the sides as #10sqrt8# ft. We need to find the hypotenuse.

Just like any other right triangle, we can use the Pythagorean theorem:

#c^2=a^2+b^2#,

where:

#c# is the hypotenuse, and #a# and #b# are the other two sides.

Plug in the known values and solve for #c#.

#c^2=(10sqrt8)^2 + (10sqrt8)^2=#

#c^2=(100xx8) + (100xx8)=#

#c^2=800 + 800=#

#c^2=1600#

Solve for #c# by taking the square root of both sides.

#c=sqrt1600#

#c="40 ft"# #larr# Remember to add the unit to the final answer.