Question

the total area of the figure to the right is 120 cm². use this fact to write an equation involving x. then solve the equation to find the value of x. the equation is □.

Explanation:

Step1: Calculate area of large rectangle

The large rectangle has length $(x + 9)$ cm and width $(x+7)$ cm. So its area $A=(x + 9)(x + 7)$ cm².

Step2: Set up the equation

Since the area of the figure is 120 cm², we have the equation $(x + 9)(x + 7)=120$.
Expand the left - hand side: $x^{2}+7x+9x + 63=120$.
Combine like terms: $x^{2}+16x+63 - 120=0$.
Get the quadratic equation: $x^{2}+16x - 57=0$.

Step3: Solve the quadratic equation

Factor the quadratic equation: $x^{2}+16x - 57=(x + 19)(x - 3)=0$.
Set each factor equal to zero: $x+19 = 0$ gives $x=-19$; $x - 3=0$ gives $x = 3$.
Since length cannot be negative, we discard $x=-19$.

Answer:

$x = 3$