If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangle in terms of x?

Hi,

An isosceles triangle is a triangle containing two sides of same length & one side of larger length.

Suppose we have a  isosceles triangle ABC as depicted in the figure attached.

Here we see that side AB is equal to the side BC

The angle at point  A is same as the angle at point C that is almost 45 degrees, Moreover, triangle BDC and ABD are also isosceles.

                       If: BD=AD=x , then , BD=DC=x

We can see in the figure that AC is equal to AD+ DC

Which means,                  AC= x+ x= 2x

Now we need to find out the length of AB, here we will use Pythagorean Theorem.

                                    AC^2 = AB^2 + BC^2

Since BC= AB, so we can write it as:

                                    AC^2 = 2AB^2

Taking sq. root on both sides

                                        AC= 2AB

                                        AB= AC/√2

Putting the value of AC as 2x

                                        AB=  2x/√2

Which means                 AB= x√2

Therefore,the length of one leg of the large right triangle in terms of x will be x√2

Hope it helps!