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.

00:00 Find the perimeter of the large rectangle

00:03 Opposite sides are equal in a rectangle

00:10 The perimeter of the rectangle equals the sum of its sides

00:16 This is the perimeter of the small rectangle

00:20 Let's mark the rectangles with numbers 1,2

00:23 The rectangles are similar according to the given data

00:28 The similarity ratio equals the ratio of perimeters

00:34 We'll substitute appropriate values and solve for the perimeter

00:42 We'll isolate the perimeter P

01:04 And this is the solution to the question

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