Given the problem, you're trying to equate the area of a rectangle to the area of a triangle, where both areas are expressed in terms of $x$. Here's how to approach the setup:

Rectangle:

• Length: $5x + 2x = 7x$ inches
• Width: 10 inches
• The area $A_{\text{rectangle}}$ of a rectangle is calculated by: $A_{\text{rectangle}} = \text{Length} \times \text{Width} = (7x)(10) = 70x \, \text{square inches}$

Triangle:

You haven't provided specific information about the triangle (e.g., its base and height), but let's assume its area is given in square inches as $A_{\text{triangle}}$. The area of a triangle is calculated by: $A_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height}$

To set up an equation to solve for $x$, you equate the area of the rectangle and the area of the triangle: $A_{\text{rectangle}} = A_{\text{triangle}}$ $70x = A_{\text{triangle}}$

This equation allows you to solve for $x$ once you know the area of the triangle.

To solve for $x$:

1. If you have more information about the triangle (e.g., its base and height), substitute those values into the equation for $A_{\text{triangle}}$ and solve for $x$.

2. The equation for $x$ would look something like: $70x = \frac{1}{2} \times \text{Base} \times \text{Height}$

Next Steps:

• Do you have any details on the base and height of the triangle?
• Alternatively, is the area of the triangle provided directly?

Related Questions:

1. What would the equation look like if the base and height of the triangle were both functions of $x$?
2. How would the equation change if the rectangle had a different width?
3. What happens if the triangle's area is expressed as $Ax + B$ (a linear expression)?
4. How can you express the length, width, and height of a rectangle in terms of functions of $x$?
5. What if the area of the rectangle was modified to include another variable?

Tip: Always simplify expressions as much as possible before equating them!