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Question

In the adjoining figure, $ AE = DC = 13 cm BE = 5 cm, \angle ABC=90°\& AD = EC = x cm$. Calculate the length of $ AB$ & the value of $ x$.

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Solution

Step 1: Analyze ABE

In triangleABE,

Given: AE=13cm,BE=5cm,ABE=90°

AE2=AB2+BE2

169=AB2+25

AB2=16925

AB2=144

AB=12cm

Step 2: Analyze DBC

In DBC

Given, DC=13cm,BE=5cm,DBC=90°

and, AD=EC=xcm

From the figure, we can see that

DB=AB-x and BC=BE+x

Step 3: Calculate x

DC2=DB2+BC2

132=AB-x2+BE+x2

169=12-x2+5+x2

169=144-24x+x2+25+10x+x2

169=169-14x+2x2

14x=2x2

x=2x72x

x=7cm

Hence, the value of x is 7cm.


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