Question

(i) Determine if the triangles below are similar, and explain how you know.
(ii) Find the lengths of the missing sides. All measures are centimeters unless otherwise
stated.

Answer 1

d = 12 cm

Step-by-step explanation:

Let small triangle and large triangles be given by $\triangle _1\:\&\: \triangle _2$

Let the Marked angels of $\triangle _1$ be

$\angle 1\: \&\: \angle 2$

Similarly Marked angels of $\triangle _2$ be $\angle 3\: \&\: \angle 4$

$\therefore \angle 1\cong \angle 3...(given) \\

\& \angle 2\cong \angle 4...(given) \\

\therefore \triangle _1\sim \triangle _2.. (By\: AA\:Postulate) \\

\therefore \frac{5}{15}=\frac{4}{d}..(By\: csst) \\

\therefore d =\frac{15\times 4}{5} \\

\therefore d =3\times 4\\

\huge \purple {\boxed {\therefore d =12\: cm}}$