Question

In the similar quadrilaterals below, what is the length of AB

10 cm
2.5 cm
8 cm
3 cm

Answer 1

Side AB is 10 cm.

Explanation:

The given quadrilaterals ABCD and EFGH are similar.

From the given figure, we can observe the following angles and sides are corresponding.

`\angle A = \angle E=90^\circ\\\angle B = \angle F=63^\circ\\\angle C = \angle G=117^\circ\\\angle D = \angle H=90^\circ`

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

`\Rightarrow (AB)/(5) = (2)/(1)\\\Rightarrow AB = 10 cm`

So, side AB is 10 cm.