Question

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In the given figure if angle PQC =angle ABC =90°. if AC= 8 cm , PC=12cm ,QC = x+1 and BC=2x+1,then find the value of x​

Answer 1

Answer:

Step-by-step explanation:

In a right angled triangle, Hypotenuse  

2

=base  

2

+height  

2

 

So, AC  

2

=AB  

2

+BC  

2

 

⇒(x+15)  

2

=(x+8)  

2

+(x+1)  

2

 

⇒x  

2

+225+30x=x  

2

+64+16x+x  

2

+1+2x

⇒225+30x=x  

2

+65+18x

⇒x  

2

−160−12x=0

⇒x  

2

−20x+8x−(20×8)=0

⇒x(x−20)+8(x−20)=0

⇒(x−20)(x+8)=0

⇒x=20  or −8  

Since, length cannot be negative,

x=20  

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