Calculate the Perimeter: Similar Rectangles with Base 14 Units

Question

Look at the two similar rectangles below and calculate the perimeter of the larger rectangle.

00:06 Let's find the perimeter of the large rectangle.

00:09 Remember, opposite sides in a rectangle are equal.

00:16 So, the perimeter is the sum of all the sides.

00:22 Now, this is the perimeter of the small rectangle.

00:26 Let's label the rectangles as one and two.

00:29 The rectangles are similar. That's given to us.

00:34 The similarity ratio is the same as the ratio of their perimeters.

00:40 We will substitute the right values and find the perimeter.

00:48 Next, we'll isolate the perimeter, represented by P.

01:10 And that's how we solve this problem.

Let's remember that in a rectangle there are two pairs of parallel and equal sides.

We will call the small triangle 1 and the large triangle 2.

We calculate the perimeter of the small triangle:

$P_1=2\times3.5+2\times1.5=10$ Since we know that the rectangles are similar:

$\frac{3.5}{14}=\frac{p_1}{p_2}$

We place the data we know for the perimeter:

$\frac{3.5}{14}=\frac{10}{p_2}$

$\frac{3.5}{14}\times p_{_2}=10$

$p_2=10\times\frac{14}{3.5}$

$P_2=40$

40 cm