Question

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

Answer 1

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

Answer 2

we know that in rt. triangle hypotenuse =perpendicular×base
according to question,
altitude is 7-x
base is X
7-x+X=13
X=13-7+X
X=6ans.