Question

The diagram shows two rectangles.

The combined area of both rectangles is

By considering the areas of the two rectangles, find an equation in the form that satisfies .

Answer 1

We know that :

⊕ Area of a Rectangle is given by : Length × Width

Let us calculate the Area of the Rectangle in the Left side of the figure

⇒ Area of Left Rectangle : (x - 3) (x + 2x)

⇒ Area of Left Rectangle : (x - 3) (3x)

⇒ Area of Left Rectangle : 3x² - 9x

Let us calculate the Area of the Rectangle in the right side of the figure

⇒ Area of the Right Rectangle : (x - 1)(x)

⇒ Area of the Right Rectangle : x² - x

Given : Combined area of both rectangles is 50 cm²

⇒ 3x² - 9x + x² - x = 50

⇒ 4x² - 10x = 50

⇒ 2x² - 5x - 25 = 0

Comparing the above equation with ax² + bx + c = 0,

we can notice that :

→ a = 2

→ b = -5

→ c = -25