Question

I need help on this question help please

Answer 1

The question shows three triangles (all right angled triangles).

Two of them are inscribed inside a bigger one.

Triangle DEB and triangle BEF are both inscribed inside the larger triangle DEF.

We shall use the ratios of these triangles to calculate the unknown sides;

`\begin{gathered} (DB)/(ED)=(DE)/(DF) \\ (DB)/(4)=(4)/((DB+4+DB)) \\ (DB)/(4)=(4)/(4+2DB) \\ \text{Cross multiply and you'll have,} \\ DB(4+2DB)=16 \\ 4DB+2DB^2=16 \\ Factorize\text{ the left hand side} \\ 2(2DB+DB^2)=16 \\ \text{Divide both sides by 2} \\ 2DB+DB^2=8 \\ \text{Subtract 8 from both sides} \\ DB^2+2DB-8=0 \\ We\text{ now have a quadratic equation, and the factors are,} \\ (DB+4)(DB-2)=0 \\ \text{Therefore, } \\ DB+4=0 \\ DB=-4 \\ OR,DB-2=0 \\ DB=2 \end{gathered}`

The length of DB is 2