Question

A triangle has a base x and height y. The hypotenuse is 12 and the area is 24. What is x and y using quadratic equation to solve?

Answer 1

there are 2 equations :
x^2 + y^2 = 12^2
1/2 * x * y = 24

Answer 2

from the 2nd : get
1/2 x y = 24
xy = 48
y = 48/x

Answer 3

subtitute y = 48/x into the 1st equation :
x^2 + y^2 = 12^2
x^2 + (48/x)^2 = 144
x^2 + 2304/x^2 = 144

then let u = x^2, so the equation can be
u + 2304/u = 144
multiply by u on both sides, get
u^2 + 2304 = 144u or
u^2 - 144u + 2304 = 0
solve for u, first. can you ?

Answer 4

by pythagorse theorm
base^2+height^2=hypotenuse^2