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Pearson Geometry Common Core, 2011

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Pearson Geometry Common Core, 2011 View details

Chapter Test

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Exercise 3 Page 537

Use the Pythagorean Theorem.

x=11sqrt(2)/2, y=11sqrt(2)/2

Practice makes perfect

To find the missing side of the triangle, we will use the Pythagorean Theorem. a^2+b^2=c^2

In the formula, a and b are the legs and c is the hypotenuse of a right triangle. We are given a triangle with a=x, b=y, and c=11.

Notice that, the legs of our triangle are congruent. Therefore, we know that x=y. Let's substitute these values into the formula.

a^2+b^2=c^2

SubstituteValues

Substitute values

x^2+ y^2= 11^2

x= y

y^2+ y^2= 11^2

▼

Solve for y

Add terms

2y^2=11^2

.LHS /2.=.RHS /2.

y^2=11^2/2

sqrt(LHS)=sqrt(RHS)

y=sqrt(11^2/2)

sqrt(a/b)=sqrt(a)/sqrt(b)

y=sqrt(11^2)/sqrt(2)

SqrtPowToNumber

sqrt(a^2)=a

y=11/sqrt(2)

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

y=11sqrt(2)/sqrt(2)* sqrt(2)

sqrt(a)* sqrt(a)= a

y=11sqrt(2)/2

Because x=y, we know that x= 11sqrt(2)2. Since a negative side length does not make sense, we only need to consider positive solutions.