Hey there :)
We are given the information saying they are similar triangles
This means we can create a ratio of sides
Bigger Δ : Smaller Δ
Side 1 | 18 : 6
Side 2 | 24 : unknown
Side 3 | unknown : x
Sincw, we know theside 1 lengths of both triangles, we can find the ratio
[tex] \frac{18}{6} [/tex] = 3
So, the bigger triangle is 3 times larger than the smaller triangle
Before, we work with x, notice that we are not given the length of the corresponding side of x in the bigger triangle. Which means, since we know the scale factor ( × 3 ), we can find side 2 to find the length of the corresponding unknown of the smaller triangle
24 : unknown = 3 → [tex] \frac{24}{unknown} = 3 [/tex]
Make "unknown" the subject
[tex] \frac{24}{3} = unknown[/tex]
unknown length of small triangle = 8
We know the base length of the small Δ to be 6, the longer side to be 8, we still need to find x.
Since x is the hypotenuse, we can use Pythagoras theorem:
( side 1 )² + ( side 2 )² = ( hypotenuse )²
( 6 )² + ( 8 )² = ( x )²
36 + 64 = x²
100 = x²
√100 = √x²
x = 10
