Let's denote the width of the smaller shape as x.
We are given that the area of the larger shape is 295c * m^2 and its width is 17 cm.
So, the length of the larger shape is 295c * m^2 / 17 cm.
Since the shapes are mathematically similar, their corresponding sides are proportional. Thus, we can write the following equation:
(x cm) / (295c * m^2 / 17 cm) = sqrt((159.5c * m^2) / (295c * m^2))
Simplifying this equation, we get:
(x cm) / (295c * m^2 / 17 cm) = sqrt(159.5c / 295c)
(x cm) / (295c * m^2 / 17 cm) = sqrt(159.5 / 295)
Now, cross-multiplying and simplifying the equation, we get:
(x cm) * 17 cm = sqrt(159.5 / 295) * (295c * m^2)
17x cm^2 = sqrt(159.5 / 295) * 295c * m^2
Now, dividing both sides of the equation by 17, we find:
x cm = (sqrt(159.5 / 295) * 295c * m^2) / 17
Hence, the width of the smaller shape is (sqrt(159.5 / 295) * 295c * m^2) / 17 cm.
The diagram shows two mathematically similar shapes with areas 295c * m ^ 2 and 159.5c * m ^ 2
The width of the larger shape is 17 cm.
Calculate the width of the smaller shape.
1 answer
1 answer