Find Rectangle's Side Length: Given Area 21 cm² and Side Sum 14 cm

Question

What is the length of the second side in a rectangle, given that the sum of the 2 opposite sides is 14 cm and the area of the rectangle is 21 cm²?

00:00 Find the second side in the rectangle

00:03 Let's draw the rectangle

00:07 In a rectangle, opposite sides are equal

00:12 Sum of opposite sides according to the given data

00:17 Let's isolate X

00:21 This is the length of side X in the rectangle

00:28 In a rectangle opposite sides are equal, let's mark it as Y

00:32 The area of the rectangle according to the given data

00:35 Let's use the formula for calculating rectangle area (side times side)

00:38 Let's substitute appropriate values according to the data and solve for Y

00:41 Let's isolate Y

00:46 And this is the solution to the question

If we are given that two opposite sides of the rectangle sum to 14

and in a rectangle, each pair of opposite sides are equal to each other, we will calculate the size of each one as follows:

$14:2=7$

We will call the other two opposite sides y and find the unknown as follows:

$7\times y=21$

We will divide both sides by 7 and get:

$y=3$