Q5: The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Q5: The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Answer:  Let the base =   x cm

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