Exercise 14 Page 644

We are told that a 45^(∘)-45^(∘)-90^(∘) triangle has a hypotenuse length of 9 and we want to find the length of its leg. To do so, we will start by drawing a diagram to illustrate the situation. Let x be the length of the leg of the triangle.

In a 45^(∘)-45^(∘)-90^(∘) triangle, the legs are congruent and the hypotenuse is sqrt(2) times the length of a leg. With this information, we can find the value of x.

9= sqrt(2) * x

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Solve for x

DivEqn

.LHS /sqrt(2).=.RHS /sqrt(2).

9/sqrt(2)=x

ExpandFrac

a/b=a * sqrt(2)/b * sqrt(2)

9sqrt(2)/sqrt(2)* sqrt(2)=x

MultSqrt

sqrt(a)* sqrt(a)= a

9sqrt(2)/2=x

RearrangeEqn

Rearrange equation

x=9sqrt(2)/2

We have that the length of the leg of our triangle is 9sqrt(2)2.