Question

The length of Rectangle A is 7x + 11. The length of Rectangle B is 15x - 9. Given the two rectangles are congruent, what is the value of x?

Answer 1

Given:

• Length of rectangle A = 7x + 11

,

• Length of rectangle B = 15x - 9

Let's find the value of x given that the two rectangles are congruent.

Since the two rectangles are congruent, the lengths of the rectangles will be equal.

Thus, we have:

Length of rectangle A = Length of rectangle B.

7x + 11 = 15x - 9

Let's solve for x using the given equation.

Subtract 15x from both sides:

7x - 15x + 11 = 15x - 15x - 9

-8x + 11 = -9

Subtract 11 from both sides:

-8x + 11 - 11 = -9 - 11

-8x = -20

Divide both sides by -8:

`\begin{gathered} (-8x)/(-8)=(-20)/(-8) \\ \\ x=2.5 \end{gathered}`

Therefore, the value of x is 2.5

ANSWER:

x = 2.5