Question

hypotenuse 26 height 14 more than base find area

Answer 1

let the base = x
height =x+14
Hypotenuse =26
(base)^2+(height)^2 =(hypotenuse)^2
x^2+(x+14)^2=(26)^2
x^2+x^2+28x+196=676
2x^2+28x+196-676=0
2x^2+28x-480=0
x^2+14x-240=0
solve the equation
find x
area =(base*height)/2

Answer 2

let base=x
then, height=x+14
by pythagoras thm.
    (26)^2=x^2+(x+14)^2
or 676=x^2+x^2+28x+196
or 2x^2+28x-480=0
or x^2+14x-240=0
or x^2+24x-10x-240=0
or x(x+24)-10(x+24)=0
or (x+24) (x-10)=0
or x= -24 or x=10

ignore x= -24, because length can't be negative.

therefore, base =10 and height = 24