Question

What is the length of the hypotenuse of the triangle 18 units 18 StartRoot 2 EndRoot units 36 units 36 StartRoot 2 EndRoot units.

Answer 1

The length of the hypotenuse is $36\sqrt{2}$.

Given that

Consider triangle DEF.

The legs have a length of 36 units each.

Triangle DEF is shown.

Angle DFE is 90 degrees and angles FDE and DEF are 45 degrees.

The lengths of sides DF and FE are 36 units.

We have to determine

What is the length of the hypotenuse of the triangle?

According to the question

The length of the hypotenuse is determined by using the Pythagoras theorem following all the steps given below.

The length of the hypotenuse is determined by;

$\rm (Hypotenuse)^2= (Base)^2+(Perpendicular)^2\\\\ (Hypotenuse)^2= (36)^2+(36)^2\\\\ (Hypotenuse)^2= 1296+1296\\\\ (Hypotenuse)^2= 2592\\\\ Hypotenuse = \sqrt{2592}\\\\ Hypotenuse = \sqrt{2\times 4 \times 4\times 9\times 9}\\\\ Hypotenuse= 9 \times 4 \times \sqrt{2}\\\\ Hypotenuse= 36 \sqrt{2}$

Hence, the length of the hypotenuse is $36\sqrt{2}$.

To know more about Pythagoras theorem click the link given below.

brainly.com/question/13963715