Exercise 49 Page 626

Let's begin with recalling the Geometric Mean Altitude Theorem. The altitude drawn to the hypotenuse of a right triangle separates the hypotenuse into two segments. The length of this altitude is the geometric mean between the lengths of these two segments.

Now, let's take a look at the given picture.

Using the theorem we recalled at the beginning, we can write a proportion. 8/x=x/4 We can solve for x using cross multiplication.

8/x=x/4

CrossMult

Cross multiply

8*4=x* x

Multiply

Multiply

32=x^2

RearrangeEqn

Rearrange equation

x^2=32

Our next step will be to take a square root of both sides of the equation. Notice that, since x represents a dimension, we will consider only positive case when taking a square root of x^2.

x^2=32

SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(x^2)=sqrt(32)

SqrtPowToNumber

sqrt(a^2)=a

x=sqrt(32)

CalcRoot

Calculate root

x=5.65685...

RoundDec

Round to 2 decimal place(s)

x≈5.66

The value of x is approximately 5.66. As we can see, both Aiden and Tia have different answers. Therefore, neither of them is correct.