Question

Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and AC = 5x - 9, what is x? Round to the nearest tenth. (1 point)
09.0
9.4
10.0
6.4

Answer 1

Similar shapes may or may not be congruent.

The value of x is (a) 9.0

The corresponding sides are:

• AB and DE
• BC and EF
• AC and DF

The side lengths are:

$\mathbf{DE = 41}$

$\mathbf{EF = 23}$

$\mathbf{DF = 36}$

$\mathbf{AC = 5x - 9}$

Because the shapes are congruent, and AC corresponds to DF.

This means that:

$\mathbf{AC = DF}$

So, we have:

$\mathbf{5x - 9 = 36}$

Collect like terms

$\mathbf{5x = 9 + 36}$

$\mathbf{5x = 45}$

Divide both sides by 5

$\mathbf{x = 9.0}$

Hence, the correct option is (a) 9.0

Read more about congruent triangles at:

brainly.com/question/12413243