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?

We Know, isosceles triangle has two same sides & one larger side.
It would be: larger side = √x + √x = √2 x

So, your final answer is √2x

Hope this helps

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isyllus isyllus · Answer 2 · 2019-05-10T11:28:46+02:00

Answer:

The length of one leg of the larger right triangle be [tex]\sqrt{2}x[/tex] unit.

Step-by-step explanation:

If the altitude of an isosceles right triangle has a length of x units.

The legs of right angle triangle are x units.

In right angle triangle altitude is one side of triangle.

Base (B) = x and Perpendicular (P) = x

Let hypotenuse (H) be y units

Using pythagoureous theorem

[tex]H^2=P^2+B^2[/tex]

[tex]y^2=x^2+x^2[/tex]

[tex]y^2=2x^2[/tex]

[tex]y=\sqrt{2}x[/tex]

Hence, The length of one leg of the larger right triangle be [tex]\sqrt{2}x[/tex] unit.