Question

the hight of right angle triangle is7cm less than its base and hypotance is 13​

Answer 1

Answer:

Given that The altitude of a right triangle is 7 cm less than its base:-

Altitude is =   x - 7 cm

Given that hypotenuse = 13cm.

Applying Pythagoras theorem,    

base2+ altitude2 = hypotenuse2

plug the values  we get    

    x2+ (  x – 7)2 = 132  

   x2+   x2+ 49 – 14  x = 169  

   2  x2 – 14  x + 48 – 169 = 0  

   2  x2 – 14  x  – 120 = 0  

Divide   by 2 to both side to simplify it  

   x2 – 7  x  – 60 = 0  

     x2 – 12  x + 5  x – 60 = 0  

     x (  x – 12) + 5 (  x – 12) = 0  

   (  x – 12)(  x + 5) = 0  

   x – 12 = 0 or   x + 5 = 0  

   x = 12 or   x = –5  

length can not negative so that x can not equal to – 5

base     x = 12cm

altitude = 12 – 7 = 5cm

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