c. \( A=h\left(\frac{a+b}{2}\right) \quad \) Solve for \( b \) given \( A=10, h=4 \) and \( a=3 \). + Workspace + Check answer

### Workspace We are given the equation: \[ A = h\left(\frac{a + b}{2}\right) \] **Given:** - \( A = 10 \) - \( h = 4 \) - \( a = 3 \) **Step 1:** Substitute the known values into the equation. \[ 10 = 4\left(\frac{3 + b}{2}\right) \] **Step 2:** Simplify the equation. \[ 10 = 4 \times \frac{3 + b}{2} \] \[ 10 = \frac{4(3 + b)}{2} \] \[ 10 = 2(3 + b) \] **Step 3:** Divide both sides by 2 to isolate \( (3 + b) \). \[ \frac{10}{2} = 3 + b \] \[ 5 = 3 + b \] **Step 4:** Solve for \( b \). \[ b = 5 - 3 \] \[ b = 2 \] ### Answer \( b = 2 \) ### Check Answer Let's verify the solution by substituting \( b = 2 \) back into the original equation. \[ A = h\left(\frac{a + b}{2}\right) \] \[ 10 = 4\left(\frac{3 + 2}{2}\right) \] \[ 10 = 4\left(\frac{5}{2}\right) \] \[ 10 = 4 \times 2.5 \] \[ 10 = 10 \] The left-hand side equals the right-hand side, confirming that \( b = 2 \) is the correct solution.