Exercise 14 Page 96

We know that a wide-screen television measures 36 inches by 54 inches. A movie theater measures 42 feet by 63 feet. We want to know if both screens are similar. To do so, let's start by calculating the area of each screen. The screens are rectangles, so we can use the formula for the area of a rectangle. A=b * h Let's calculate the area of each screen. First, let's do the wide-screen television. We will substitute b=36 and h=54 into the formula and calculate the area. The area of the TV screen is 1944 inches. Now, we will substitute b=42 and h=63 into the formula to calculate the area of the movie theater screen.

A=b * h

SubstituteII

b= 42, h= 63

A= ( 42)( 63)

Multiply

Multiply

A=2646

Remember that when two figures are similar, the value of the ratio of their areas is equal to the square of value of the ratio of their corresponding sides lengths. Area A/Area B=(Side Length A/Side Length B)^2 We will consider that the corresponding sides lengths are 36 and 42. The areas are 1944 and 2646. Let's substitute these values into the above relation to see if both screens are similar. 1944/2646=(36/42)^2 We can simplify this equation by calculating the power of the quotient.

1944/2646=(36/42)^2

a^m/b^m=(a/b)^m

1944/2646=36^2/42^2

CalcPow

Calculate power

1944/2646=1296/1764

ReduceFrac

a/b=.a /36./.b /36.

36/49=36/49

This means that both screens are similar.