Answer:
Side AB is 10 cm.
Step-by-step explanation:
The given quadrilaterals ABCD and EFGH are similar.
From the given figure, we can observe the following angles and sides are corresponding.
[tex]\angle A = \angle E=90^\circ\\\angle B = \angle F=63^\circ\\\angle C = \angle G=117^\circ\\\angle D = \angle H=90^\circ[/tex]
Ratio of corresponding sides will be equal:
AB:EF = BC: FG = CD:GH = DA:HE
We have to find the side AB.
Given the sides
EF = 5 cm
BC = 9 cm
DA = 8 cm
EH = 4 cm
So, ratio DA:EH = 8:4 = 2:1
We know that ratio of corresponding sides will be same:
AB:EF = DA:EH
[tex]\Rightarrow \dfrac{AB}{5} = \dfrac{2}{1}\\\Rightarrow AB = 10 cm[/tex]
So, side AB is 10 cm.
