Complete question is attached.
Answer:
a) ED = 6.5 cm
b) BE = 14.4 cm
Step-by-step explanation:
From the triangle, we are given the following dimensions:
AB = 20 cm
BC = 5 cm
CD = 18 cm
AE = 26 cm
We are asked to find length of sides ED and BE.
a) Find length of ED.
From the triangle Let's use the equation:
[tex] \frac{AB}{BC} = \frac{AE}{ED} [/tex]
Cross multiplying, we have:
AB * ED = AE * BC
From this equation, let's make ED subject of the formula.
[tex] ED = \frac{AE * BC}{AB} [/tex]
Let's substitute figures,
[tex] ED = \frac{26 * 5}{20} [/tex]
[tex] ED = \frac{130}{20} = 6.5[/tex]
Therefore, length of ED is 6.5 cm.
b) To find length of BE, let's use the equation:
[tex] \frac{AB}{AC} = \frac{BE}{CD} [/tex]
Cross multiplying, we have:
AB * CD = AC * BE
Let's make BE subject of the formula,
[tex] BE = \frac{AB * CD}{AC} [/tex]
From the triangle, length AC = AB + BC.
AC = 20 + 5 = 25
Substituting figures, we have:
[tex] BE = \frac{20 * 18}{25} [/tex]
[tex] BE = \frac{360}{25} = 14.4 [/tex]
Therefore, length Of BE is 14.4cm
