Question

Find the length of AB, given that triangle ABC is congruent to triangle DEF

Answer 1

(C) 22

Explanation:

Given that triangle ABC is congruent to triangle DEF, then the corresponding sides are equal in length:

• 
  `\sf \overline{AB}=\overline{DE}`
• 
  `\sf \overline{BC}=\overline{EF}`
• 
  `\sf \overline{AC}=\overline{DF}`

To find the length of
`\sf \overline{AB}`, first find the value of x by setting the expressions for
`\sf \overline{AB}` and
`\sf \overline{DE}` equal to each other and solving for x:

`\begin{aligned}\sf \overline{AB}&=\sf \overline{DE}\\7x+1&=9x-5\\7x+1-7x&=9x-5-7x\\1&=2x-5\\1+5&=2x-5+5\\6&=2x\\x&=3\end{aligned}`

Now, substitute the found value of x into the expression for
`\sf \overline{AB}`:

`\overline{\sf AB}=7(3)+1`

`\overline{\sf AB}=21+1`

`\overline{\sf AB}=22`

Therefore, the length of
`\sf \overline{AB}` is 22 units.

Answer 2

C. 22

Explanation:

To find the length of
`\sf \overline{AB }`, we can use the fact that ∆ ABC is congruent to ∆ DEF.

This means that the corresponding sides of the two triangles are equal in length.

Therefore,
`\sf \overline{AB} = \overline{DE}`.

We can also use the given equation to solve for the length of
`\sf \overline{AB }`.

The equation is:

7x + 1 = 9x - 5

Subtracting 7x from both sides of the equation, we get:

7x + 1 - 7x = 9x - 5 - 7x

1 = 2x - 5

Adding 5 to both sides of the equation, we get:

1 + 5= 2x - 5 + 5

6 = 2x

Dividing both sides of the equation by 2, we get:

`\sf (6)/(2)=(2x)/(2)`

3 = x

x = 3

Substituting x = 3 into the equation
`\sf \overline{AB} = \overline{DE}`, we get:

`\sf \overline{AB} = \overline{DE} = 7(3) + 1 = 21 + 1 = 22`

Therefore, the length of
`\sf \overline{AB }` is C. 22.