In a triangle ABC,D and E …

We have,

DE || BC
Now, In {tex}\triangle{/tex}ADE and {tex}\triangle {/tex}ABC
{tex}\angle A = \angle A{/tex} [common]
{tex}\angle A D E = \angle A B C{/tex} [{tex}\because{/tex} DE || BC {tex}\Rightarrow{/tex} Corresponding angles are equal]
{tex}\Rightarrow \triangle A D E= \triangle A B C{/tex} [By AA criteria]
{tex}\Rightarrow \frac { A B } { B C } = \frac { A D } { D E }{/tex} [{tex}\because{/tex} Corresponding sides of similar triangles are proportional]
{tex}\Rightarrow \frac { A B } { 5 } = \frac { 2.4 } { 2 }{/tex}
{tex}\Rightarrow A B = \frac { 2.4 \times 5 } { 2 }{/tex}
{tex}\Rightarrow{/tex} AB = 1.2 {tex}\times{/tex} 5
= 6.0 cm
{tex}\Rightarrow{/tex} AB = 6 cm
{tex}\therefore{/tex} BD = AB - AD
= 6 - 2.4
= 3.6 cm
{tex}\Rightarrow{/tex} DB = 3.6 cm
Now,
{tex}\frac { A C } { B C } = \frac { A E } { D E }{/tex} [{tex}\because{/tex} Corresponding sides of similar triangles are equal]
{tex}\Rightarrow \frac { A C } { 5 } = \frac { 3.2 } { 2 }{/tex}
{tex}\Rightarrow A C = \frac { 3.2 \times 5 } { 2 }{/tex}
= 1.6 {tex}\times{/tex} 5
= 8.0 cm
{tex}\Rightarrow{/tex} AC = 8 cm
{tex}\therefore{/tex} CE = AC - AE
= 8 - 3.2
= 4.8 cm
Hence, BD = 3.6 cm and CE = 4.8 cm