A rectangle has a measurement of 15 cm long and 9 cm wide. Label another rectangle that is similar and why are they similar?
pick any rectangle whose sides are the same multiple of 9 and 15
for example, .9 and 1.5
or 90 and 150
they are similar because that's what similar means: corresponding sides are in the same ratio.
corresponding angles are equal, because both figures are rectangles.
To label another rectangle that is similar to the given rectangle, we need to understand what it means for two rectangles to be similar.
Two rectangles are considered similar if they have the same shape but may differ in size. In other words, the corresponding angles of similar rectangles are congruent and the ratio of corresponding side lengths is constant.
In the given rectangle, the length is 15 cm and the width is 9 cm. To create a similar rectangle, we can maintain the same ratio of side lengths, but change the actual value of the lengths.
Let's assume the ratio of the lengths of the two rectangles is 'k'. We can find a value of 'k' by dividing the length of the new rectangle by the length of the given rectangle. So, let's say the length of the new rectangle is 'x'. Then, we have the equation:
x/15 = k
To find the corresponding width of the new rectangle, we multiply the width of the given rectangle by 'k'. So, the width of the new rectangle is:
9 * k
By choosing different values for 'k', we can create multiple similar rectangles. For example, let's consider a value of 'k' as 2. If we substitute this value into the equations, we can find the dimensions of the new rectangle.
x/15 = 2 => x = 30
9 * k = 9 * 2 = 18
So, the dimensions of the new rectangle are 30 cm long and 18 cm wide. These two rectangles are similar because their corresponding angles are congruent and the ratio of their side lengths is constant (2:1).