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Trava [24]
3 years ago
9

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 triangl

e in terms of x? x units x units x units 2x units

Mathematics
2 answers:
SVETLANKA909090 [29]3 years ago
3 0

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}

marusya05 [52]3 years ago
3 0

Answer:

b)x/2

Step-by-step explanation:

took the test

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