Start by finding the scale factor between the ornaments.
300 square inches
Practice makes perfect
We are given that two picture frames are similar. We are asked to find the area of the larger frame knowing that the area of the smaller frame is 108 square inches. Let's start by recalling the relationship between the areas of similar figures.
Area of Similar Figures
If figure B is similar to figure A by a scale factor, then the area of B is equal to the area of A times the square of the scale factor.
Therefore, to get the area of the larger frame, we need to multiply the area of the smaller frame by the scale factor raised to the second power.
Area of the larger frame
= 108( Scale factor)^2 [0.3em]However, we do not know the scale factor. To find it, we can use the ratio of the perimeters of the two frames. Note that the ratio is less than 1.
3:5 = 3/5 < 1
Therefore, 35 is a ratio of the perimeter of the smaller frame to the
perimeter of the larger frame. For simplicity, let s represent the perimeter of the smaller frame and let l represent the perimeter of the larger frame
3/5 = s/l
Now let's recall the relationship between the perimeters of similar figures.
Perimeter of Similar Figures
If figure B is similar to figure A by a scale factor, then the perimeter of B is equal to the perimeter of A times the scale factor.
According to this rule, the perimeter of the larger frame is equal to the perimeter of the smaller frame times the scale factor.
l =
s( Scale factor)
We can rewrite this equation and use the ratio to get the scale factor.
Therefore, the scale factor is equal to 53. Now we can substitute this value into the first equation.
Area of the larger frame
= 108( 5/3)^2
Finally, we will calculate the area of the larger frame.
