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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
6. Inequalities in Two Triangles
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Exercise 46 Page 462

Use the Pythagorean Theorem.

B

Practice makes perfect

Two sides of a square and a diagonal form a right triangle.

Recall that the Pythagorean Theorem states that in a right triangle the square of the length of the hypotenuse is the sum of the square of the length of the legs. We can use this to express the length of the diagonal of a square in terms of the length of the sides.

a^2+a^2=d^2
â–¼
Solve for d
AddTerms

Add terms

2a^2=d^2
RearrangeEqn

Rearrange equation

d^2=2a^2
SqrtEqn

sqrt(LHS)=sqrt(RHS)

d=sqrt(2a^2)
SqrtProd

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

d=sqrt(2)sqrt(a^2)
SqrtPowToNumber

sqrt(a^2)=a

d=sqrt(2)a

It is given that a=x+3, let's substitute this in the expression we found.

d=sqrt(2)a
Substitute

a= x+3

d=sqrt(2)( x+3)
Distr

Distribute sqrt(2)

d=sqrt(2)x+sqrt(2)* 3
CommutativePropMult

Commutative Property of Multiplication

d=xsqrt(2)+3sqrt(2)

The correct answer is B.

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Exercises 2 (Page 457)
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