Cumulative Standards Review
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Begin by finding the width of the larger rectangle by using the formula for the area of a rectangle.
29 ft
We will first find the width of Rectangle A. We will then find the side lengths of Rectangle B using the similarity of rectangles. Only then will we able to find the perimeter of Rectangle B.
We will first use the formula for the area of a rectangle to find the width of Rectangle A.
l= 20, A= 180
.LHS /20.=.RHS /20.
Rearrange equation
Knowing the length of the larger rectangle's width, we can use the similarity between the figures to find the sides of Rectangle B. Let's call the sides of it x and y as shown below.
Now, let's use the formula for calculating a rectangle's area once more. This time, however, we will use it with regards to Rectangle B. A=x* y By substituting the expression we just found for y and 45 for A into the formula, we can solve for x.
A= 45, y= 20/9x
a*b/c= a* b/c
LHS * 9=RHS* 9
.LHS /20.=.RHS /20.
Rearrange equation
sqrt(LHS)=sqrt(RHS)
One of the sides has a length of 4.5ft. To find the other length, we substitute this value back into the equation for y.
Rectangle B has a width of 4.5ft and length of 10ft.
Finally, we can use these lengths to find the perimeter of Rectangle B.
The perimeter of rectangle B is 29ft.