Question

Find the value of x and y using the diagram below.​

Answer 1

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x = 2 , y = 3

Explanation:

As the given figure is a rectangle, therefore the opposite sides should be equal. So -

3x + y = 12 – y...(eqn (i) )

and

y – x = x – 1...(eqn (ii) )

Solving eqn (ii) we get -

→ y – x = x – 1

→ y = x + x – 1

→ y = 2x – 1...eqn(iii)

Solving eqn (i) we get -

→ 3x + y = 12 – y

→ 3x = 12 – y – y

→ 3x = 12 – 2y

Substituting the value of eqn (iii)

→ 3x = 12 – 2(2x– 1)

→ 3x = 12 – 4x + 2

→ 3x + 4x = 14

→ 7x = 14

→ x = 14/7

→ x = 2

Hope it helps you!!

Answer 2

x = 2; y = 3

Explanation:

Since the quadrilateral has 4 right angles, it is a rectangle.

In a rectangle, opposite sides are congruent.

3x + y = 12 - y

x - 1 = y - x

We have a system of two equation is 2 variables.

Let's simplify both equations.

3x + 2y = 12

2x - y = 1

Rewrite the first equation. Multiply both sides of the second equation by 2. Add the equations.

3x + 2y = 12

(+) 4x - 2y = 2

-------------------------

7x = 14

Divide both sides by 2.

x = 2

Substitute 2 for x in the second original equation and solve for y.

x - 1 = y - x

2 - 1 = y - 2

1 = y - 2

y = 3

Answer: x = 2; y = 3