Question

Q5.

The diagram shows a rectangle.
B=(x + 4) cm
H=(x-5) cm
The area of the rectangle is 90 cm².
Set up and solve a quadratic equation to work out the value of x.

Answer 1

x = 11

Explanation:

According to the question:

Base of the rectangle = (x + 4) cm

Height of the rectangle = (x - 5) cm

Area of the rectangle = 90 cm²

Area of rectangle = Height of the rectangle × Base of the rectangle

`\therefore`

`\rm \implies 90 = (x + 4)(x - 5) \\ \\ \rm \implies 90 = {x}^(2) - x - 20 \\ \\ \rm \implies {x}^(2) - x = 90 + 20 \\ \\ \rm \implies {x}^(2) - x = 110 \\ \\ \rm \implies {x}^(2) - x - 110 = 0 \\ \\ \rm \implies {x}^(2) - 11x + 10x - 110 = 0 \\ \\ \rm \implies x(x - 11) + 10(x - 11) = 0 \\ \\ \rm \implies (x - 11)(x + 10) = 0 \\ \\ \rm \implies x - 11 = 0 \: \: and \: \: x + 10 = 0 \\ \\ \rm \implies x = 11 \: or \: - 10`

As value of length cannot be negative.

Therefore, value of x should be 11