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Question

The given figure shows a quadrilateral ABCD in which AD=13cm,DC=12cm,BC=3cm and ABD=BCD=90 . Calculate the
length of AB.

1355007_44ed79f2a92945c4b101fc46e727b5c5.png

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Solution

Pythagoras theorem states that in a right angled triangle, the square on the hypotenuse is equal to the sum of of the squares on the remaining two sides.
First, we consider the ADC and applying Pathagoras theorem we get,
DB2=DC2+BC2
DB2=122+32
DB2=144+9
DB2=153
Now, we consider the ABD and applying Pathagoras theorem we get,
DA2=DB2+BA2
132=153+BA2
BA2=169153=16
BA=4
The length of AB is 4 cm

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