Question

The height of right triangle is 7cm less than its base .if the hypotenuse is 13cm form the quadratic equation to find the base of the triangle

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

Answer:

Let base = x cm and height = (x - 7) cm

Hypotenuse = 13 cm

By Pythagoras theorem,

x2 + (x - 7)2 = 132 x=12 or x=-5

x2 + 49 + x2 - 14x = 169

2x2 - 14x - 120 = 0

x2 - 12x + 5x - 60 = 0

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

X - 12 = 0 or x + 5 = 0

The other two sides are 12 cm and 5 cm.

Hope it was help full