In , lies on and lies on such that . The following measurements are known: , and…

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

\triangle ABC

D

lies on

AB

and

E

lies on

AC

such that

DE \parallel BC

. The following measurements are known:

AD = 4.5\,\text{cm}

DB = 7.5\,\text{cm}

and

AE = 6\,\text{cm}

. (i) Find the ratio

AD:DB

in simplest form. (ii) Using the result of part (i), calculate

EC

. (iii) Determine the full length of

AC