Question

find the value of x in each figure.
(1)
(2)
(3)

Explanation:

Step1: Assume the figure (1) is a trapezoid and use mid - segment formula

If a trapezoid has bases \(a\) and \(b\) and mid - segment \(m\), then \(m=\frac{a + b}{2}\). Here \(a = 13\), \(b=25\), and \(m=x\). So \(x=\frac{13 + 25}{2}\).

Step2: Calculate the value of \(x\) for figure (1)

\(x=\frac{13+25}{2}=\frac{38}{2}=19\).

Step3: Assume figure (2) is a trapezoid and use mid - segment formula

Let the bases be \(a = 8\) and \(b = 18\), and mid - segment \(m=x + 4\). Then \(x + 4=\frac{8+18}{2}\).

Step4: Solve for \(x\) in figure (2)

First, calculate \(\frac{8 + 18}{2}=\frac{26}{2}=13\). Then \(x+4 = 13\), so \(x=13 - 4=9\).

Step5: Assume figure (3) is a trapezoid and use mid - segment formula

Let the bases be \(a=2x + 1\) and \(b = 3x+2\), and mid - segment \(m=2x + 4\). Then \(2x+4=\frac{(2x + 1)+(3x+2)}{2}\).

Step6: Simplify the right - hand side of the equation for figure (3)

\(\frac{(2x + 1)+(3x+2)}{2}=\frac{2x+1 + 3x+2}{2}=\frac{5x + 3}{2}\). So \(2x+4=\frac{5x + 3}{2}\).

Step7: Cross - multiply and solve for \(x\) in figure (3)

Multiply both sides by 2: \(2(2x + 4)=5x+3\). Expand the left - hand side: \(4x+8 = 5x+3\). Subtract \(4x\) from both sides: \(8=x + 3\). Subtract 3 from both sides: \(x=5\).

Answer:

(1) \(x = 19\)
(2) \(x = 9\)
(3) \(x = 5\)