Question

In the diagram, E is the midpoint of DF. What is the value of x?

Answer 1

`\large\boxed{\mathtt{x = 10}}`

Explanation:

`\textsf{We are asked for the value of x.}`

`\textsf{Because E is a Midpoint,} \ \overline{DE} \cong \ \overline{EF}.`

`\textsf{Let's set them equal to each other.}`

`\mathtt{45=3(x+5)}`

`\large\underline{\textsf{Begin Solving:}}`

`\mathtt{45= ( 3 * x ) +(3 * 5)}`

`\mathtt{45= 3x+15}`

`\large\underline{\textsf{Subtract 15 from Both Sides:}}`

`\mathtt{3x=30}`

`\large\underline{\textsf{Divide by 3:}}`

`\large\boxed{\mathtt{x = 10}}`

Answer 2

x = 10

Explanation:

To find:-

• The value of x.

Answer:-

We are here given that, E is the midpoint of DF. The value of DE is 45 and that of EF is 3(x+5) . We are interested in finding out the value of "x" .

According to Euclid's first axiom , Things which are half of the same thing are equal to one another. So here;

`\sf:\implies DF = DF \\`

`\sf:\implies (DF)/(2)=(DF)/(2) \\`

`\sf:\implies DE = EF \\`

On substituting the respective values, we have;

`\sf:\implies 45 = 3(x+5) \\`

`\sf:\implies 45 = 3x + 15 \\`

`\sf:\implies 3x = 45-15\\`

`\sf:\implies 3x = 30 \\`

`\sf:\implies x =(30)/(3)\\`

`\sf:\implies \red{x = 10}\\`

Hence the value of x is 10 .