Question

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?

Answer 1

X square root 2

Step-by-step explanation:

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Answer 2

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!