Exercise 44 Page 388

The longest line inside a square is always its diagonal. With this information, we can illustrate the situation. The square's side, we will label a.

From the exercise, we know that the square has an area of 50 square units. Since the area of a square is calculated by squaring its side length, we can write an equation. a^2=50 Let's solve this equation for a.

a^2=50

SqrtEqn

sqrt(LHS)=sqrt(RHS)

a=± sqrt(50)

a > 0

a=sqrt(50)

When we know the sides of the square, we can find the length of the diagonal by using the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteII

a= sqrt(50), b= sqrt(50)

( sqrt(50))^2+( sqrt(50))^2=c^2

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Solve for c

PowSqrt

( sqrt(a) )^2 = a

50+50=c^2

AddTerms

Add terms

100=c^2

RearrangeEqn

Rearrange equation

c^2=100

SqrtEqn

sqrt(LHS)=sqrt(RHS)

c=± 10

c > 0

c=10