In the diagram, ABCD is a rectangle. Given that AB = $(2x + y)$ cm, BC = $(x + y)$ cm, CD = $(3x + 5y + 3)$ cm and AD = $(4x + 5y - 7)$ cm. Find the values of x and y.

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Worked solution

1. Use equality of opposite sides in a rectangle to form equations.

In a rectangle, opposite sides are equal.

$AB = CD$ :
$2x + y = 3x + 5y + 3$
$x + 4y = -3 \quad \text{(1)}$

$BC = AD$ :
$x + y = 4x + 5y - 7$
$3x + 4y = 7 \quad \text{(2)}$

2. Eliminate one variable to find $x$.

Subtract (1) from (2):
$3x + 4y - (x + 4y) = 7 - (-3)$
$2x = 10$
$x = 5$

3. Substitute $x$ back into one equation to find $y$.

Substitute $x = 5$ into (1):
$5 + 4y = -3$
$4y = -8$
$y = -2$

Answer

$x = 6,\ y = -3$

AI analysis — may contain mistakes.

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