Question

1. geometry write and solve an equation to find the value of x so that the figures have the same area.

Explanation:

Step1: Write area formulas

The area of the first parallelogram is $A_1=15\frac{3}{7}x=\frac{108}{7}x$. The area of the second parallelogram is $A_2 = 9\times(5 + x)=45+9x$.

Step2: Set areas equal

Since the areas are the same, we set up the equation $\frac{108}{7}x=45 + 9x$.

Step3: Get a common - denominator

Multiply every term in the equation by 7 to get $108x=315+63x$.

Step4: Isolate the variable

Subtract $63x$ from both sides: $108x - 63x=315$, which simplifies to $45x = 315$.

Step5: Solve for x

Divide both sides by 45: $x=\frac{315}{45}=\frac{35}{6}$.

Answer:

$x = \frac{35}{6}$