Exercise 45 Page 715

Recall that in isosceles triangles, the legs are congruent and the acute angles are also congruent. For a right isosceles triangle, by the Triangle Angle Sum Theorem, these acute angles must both measure 45^(∘). Therefore, the triangle is a 45^(∘)-45^(∘)-90^(∘) triangle.

In this type of triangle, the hypotenuse is sqrt(2) times the length of a leg. We can use this information to find the length of the hypotenuse.

sqrt(2) * 2sqrt(6)

ProdSqrt

sqrt(a)*sqrt(b)=sqrt(a* b)

2sqrt(12)

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Simplify

SplitIntoFactors

Split into factors

2sqrt(4* 3)

SqrtProd

sqrt(a* b)=sqrt(a)*sqrt(b)

2sqrt(4)* sqrt(3)

WritePow

Write as a power

2sqrt(2^2)* sqrt(3)

RootPowToNumber

sqrt(a^2)=a

2* 2* sqrt(3)

Multiply

Multiply

4sqrt(3)

Therefore, the correct answer is H.