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

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

$AC^{2} =2AB^{2}$

$AC^{2} =2AB^{2}\\\\ AB=\frac{AC}{\sqrt{2}}\\\\ AB=\frac{2x}{\sqrt{2}}\\\\ AB=x\sqrt{2}$

therefore

the answer is

the length of one leg of the large right triangle in terms of x is equal to $x\sqrt{2}$

Answer 2

Answer:

b)x/2

Step-by-step explanation:

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