Question

The two triangles in the diagram are similar.
There are two possible values of x.
Work out each of these values.
State both assumptions* you make in your working.

Answer 1

Answer:

$x = 2$

Step-by-step explanation:

you have 2 triangle and they are similar w/c is their ratio are equal .

$\frac{10}{15} = \frac{10 + x}{15 + 3}$

$\frac{2}{3} = \frac{10 + x}{18}$

$2 \times 18 = 3(10 + x)$

$36 = 30 + 3x$

$3x = 36 - 30$

$3x = 6$

$\frac{3x}{3} = \frac{6}{3}$

$x = 2$

Hope it help but it will be more helpful if u give me brainlist.

Answer 2

Answer:

1. x = 2 cm
2. x = 17 cm

Step-by-step explanation:

You want the two possible values of x given the triangles in the figure are similar.

Assumption 1

We assume the similar triangles are ∆ABE ~ ∆ACD.

The corresponding sides are proportional, so we have ...

  $\dfrac{AB}{AE}=\dfrac{AC}{AD}\\\\\\\dfrac{10}{15}=\dfrac{10+x}{18}\\\\\\x=\dfrac{10\cdot18}{15}-10=2$

x = 2 cm

Assumption 2

We assume the similar triangles are ∆ABE ~ ∆ADC.

The corresponding sides are proportional, so we have ...

  $\dfrac{AB}{AE}=\dfrac{AD}{AC}\\\\\\\dfrac{10}{15}=\dfrac{18}{10+x}\\\\\\x=\dfrac{15\cdot18}{10}-10=17$

x = 17 cm