Question

Use rhombus TQRS to answer the question.

3. What is the value of x?
A. 2
B. 1
C. 5
D. 4

4. What is the value of y?
A. 4
B. 3
C. 2
D. 1

Answer 1

B and A

Explanation:

The diagonals of a rhombus bisect each other at right angles, thus

(3)

y = x + 3 → (1)

3x + 2 = y + 1 → (2)

Substitute y = x + 3 into (2)

3x + 2 = x + 3 + 1

3x + 2 = x + 4 ( subtract x from both sides )

2x + 2 = 4 ( subtract 2 from both sides )

2x = 2 ( divide both sides by 2 )

x = 1 → B

(4)

Substitute x = 1 into (1)

y = 1 + 3 = 4 → A

Answer 2

x = 1, y = 4

Explanation:

First, we see on SQ is bisected by TR, so both sides of SQ are congruent, so

y = x + 3. Substitute x + 3 for y, then simplify.

3x + 2 = (x + 3) + 1

3x + 2 = x + 4 (Subtract x from both sides, then subtract 2 from both sides)

2x = 2 (Divide both sides by 2)

x = 1

Now substitute 1 for x in the equation y = x + 3

y = 1 + 3

y = 4