Use rhombus TQRS below for questions
what is the value of x?
what is the value of y?

The value of x is 1.

The value of y is 4.

Solution:

Given TQRS is a rhombus.

Property of rhombus:

Diagonals bisect each other.

In diagonal TR

⇒ 3x + 2 = y + 1  

⇒ 3x – y = –1 – – – – (1)

In diagonal QS

⇒ x + 3 = y

⇒ x – y = –3 – – – – (2)

Solve (1) and (2) by subtracting

⇒ 3x – y – (x – y) = –1 – (–3)

⇒ 3x – y – x + y = –1 + 3

⇒ 2x = 2

⇒ x = 1

Substitute x = 1 in equation (2), we get

⇒ 1 – y = –3

⇒ –y = –3 – 1

⇒ –y = –4

⇒ y = 4

The value of x is 1.

The value of y is 4.