Question

EF is the median of trapezoid ABD.
What is x?

Answer 1

The value of x is 6 .

Step-by-step explanation:

Solution :

Here's the required formula of median of trapezoid :

`{\implies{\pmb{\sf{Median=(Base_1 + Base_2)/(2)}}}}`

Where :

• ➝ Median
  `\rm\overline{EF}` = 15
• ➝ Base₁ (AB) = x + 1
• ➝ Base₂ (CD) = 3x + 5

Substituting all the given values in the formula to find the value of x :

`\begin{gathered}\qquad{\longrightarrow{\sf{Median =(Base_1 + Base_2)/(2)}}}\\\\\qquad{\longrightarrow{\sf{\overline{EF} =(Base_1 + Base_2)/(2)}}}\\\\\qquad{\longrightarrow{\sf{15 =((x +1) + (3x + 5))/(2)}}}\\\\\qquad{\longrightarrow{\sf{15 =((x +3x) + (1 + 5))/(2)}}}\\\\\quad{\longrightarrow{\sf{15 =((4x) + (6))/(2)}}}\\\\ \quad{\longrightarrow{\sf{15 * 2 = 4x + 6}}}\\\\\quad{\longrightarrow{\sf{30 = 4x + 6}}}\\\\\quad{\longrightarrow{\sf{4x = 30 - 6}}}\\\\\quad{\longrightarrow{\sf{4x =24}}}\\\\\quad{\longrightarrow{\sf{x = (24)/(4)}}}\\\\\quad{\longrightarrow{\sf{x =6}}}\\\\\quad{\star{\underline{\boxed{\sf{\purple{x =6}}}}}}\end{gathered}`

Hence, the value of x is 6.

`\rule{300}{2.5}`

Answer 2

• x = 6

Explanation:

The median is the average of the bases:

• 15 = 1/2(x + 1 + 3x + 5)
• 30 = 4x + 6
• 4x = 30 - 6
• 4x = 24
• x = 6