Mathematics

Problem

Triangles DEF and LMN are such that

DE = x + 1\,\text{cm}

EF = x + 3\,\text{cm}

FD = x + 5\,\text{cm}

while

LM = 2x + 2\,\text{cm}

MN = 2x + 6\,\text{cm}

and

NL = 2x + 10\,\text{cm}

. a. (i) If the perimeter of

\Delta DEF

45\,\text{cm}

, find the value of

x

and hence write the lengths of all six sides. b. (ii) Prove that

\Delta DEF

is similar to

\Delta LMN

. c. (iii) Determine the ratio of their areas.