Answer:
The value of x is 6 .
Step-by-step explanation:
Solution :
Here's the required formula of median of trapezoid :
[tex]{\implies{\pmb{\sf{Median=\dfrac{Base_1 + Base_2}{2}}}}}[/tex]
Where :
- ➝ Median [tex]\rm\overline{EF}[/tex] = 15
- ➝ Base₁ (AB) = x + 1
- ➝ Base₂ (CD) = 3x + 5
Substituting all the given values in the formula to find the value of x :
[tex]\begin{gathered}\qquad{\longrightarrow{\sf{Median =\dfrac{Base_1 + Base_2}{2}}}}\\\\\qquad{\longrightarrow{\sf{\overline{EF} =\dfrac{Base_1 + Base_2}{2}}}}\\\\\qquad{\longrightarrow{\sf{15 =\dfrac{(x +1) + (3x + 5)}{2}}}}\\\\\qquad{\longrightarrow{\sf{15 =\dfrac{(x +3x) + (1 + 5)}{2}}}}\\\\\quad{\longrightarrow{\sf{15 =\dfrac{(4x) + (6)}{2}}}}\\\\ \quad{\longrightarrow{\sf{15 \times 2 = 4x + 6}}}\\\\\quad{\longrightarrow{\sf{30 = 4x + 6}}}\\\\\quad{\longrightarrow{\sf{4x = 30 - 6}}}\\\\\quad{\longrightarrow{\sf{4x =24}}}\\\\\quad{\longrightarrow{\sf{x = \dfrac{24}{4}}}}\\\\\quad{\longrightarrow{\sf{x =6}}}\\\\\quad{\star{\underline{\boxed{\sf{\purple{x =6}}}}}}\end{gathered}[/tex]
Hence, the value of x is 6.
[tex]\rule{300}{2.5}[/tex]
