rectangle a is similar to smaller rectangle b. the scale factor is 5/3. if the area of rectangle a is 150 square inches, what is the area of rectangle b?
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To find the area of rectangle b, we can use the concept of similar figures. Since rectangle a is similar to rectangle b, the scale factor between them is 5/3. This means that the corresponding sides of rectangle b are 5/3 times smaller than those of rectangle a.
To find the area of rectangle b, we can use the formula for the area of a rectangle: Area = Length × Width.
Let's assume the length of rectangle b is x inches. Since the scale factor between the rectangles is 5/3, the length of rectangle a would be (5/3) times the length of rectangle b, or (5/3)x inches.
Next, we know that the area of rectangle a is 150 square inches. Therefore, we can set up the following equation:
Area of rectangle a = (5/3)x × Width of rectangle a
150 = (5/3)x × Width of rectangle b
Now, we can solve for the width of rectangle b:
Width of rectangle b = 150 / (5/3) = 150 * (3/5) = 90
Finally, we can calculate the area of rectangle b:
Area of rectangle b = Length × Width = x × 90 = 90x square inches.
Therefore, the area of rectangle b is 90x square inches.