Find the Values of x and y Using Properties of a Rectangle

Video Explanation

Watch the video below to understand the complete solution step by step:

Solution

Question: Find the values of x and y in the following rectangle:

13, 7, x + 3y, 3x + y

Step 1: Use the Property of a Rectangle

In a rectangle, opposite sides are equal.

So,

13 = x + 3y  …… (1)

7 = 3x + y  …… (2)

Step 2: Solve the Pair of Linear Equations

From equation (2):

y = 7 − 3x  …… (3)

Substitute y from equation (3) into equation (1):

x + 3(7 − 3x) = 13

x + 21 − 9x = 13

−8x = −8

⇒ x = 1

Step 3: Find the Value of y

Substitute x = 1 in equation (3):

y = 7 − 3(1)

y = 4

Final Answer

∴ The required values are:

x = 1 and y = 4

Conclusion

Thus, by using the property that opposite sides of a rectangle are equal, we find that the values of x and y are 1 and 4 respectively.