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? x units x units x units 2x units

Answer 1

b)x/2

Explanation:

took the test

Answer 2

the picture in the attached figure

we know that

if ABC is an isosceles triangle

then

AB=BC

angle A=angle C=45 degrees

and

triangle ABD and triangle BDC also are isosceles triangles

AD=BD=x

DC=BD=x

the hypotenuse AC is equal to

`AC=AD+DC\\ AC=x+x\\ AC=2x`

To find the length AB applying the Pythagorean Theorem

`AC^(2) =AB^(2) +BC^(2)`

remember that AB=BC

`AC^(2) =2AB^(2)`

`AC^(2) =2AB^(2)\\\\ AB=(AC)/(√(2))\\\\ AB=(2x)/(√(2))\\\\ AB=x√(2)`

therefore

the answer is

the length of one leg of the large right triangle in terms of x is equal to
`x√(2)`