Question 1044784
Hi there,
Area of a triangle is = 1/2(base x height)
Make height (altitude) = x
Base = x + 8
Area = 1/2(base x altitude)
192 = 1/2(x(x + 8))
192 = 1/2(x^2 + 8x)
Multiply both sides by 2
384 = x^2 + 8x
Rearrange into ax^2 + bx + c form
x^2 + 8x - 384 = 0
Factorise
(x - 16)(x + 24) = 0
x + 24 = x = -24 (discount as -ve)
x - 16 = 0
x = 16
Altitude = 16 m
Base = 24 m
........
Now we can work out the size of the two 
equal sides by dividing the base of 24 m
into 2 lots of 12 m.
We now have a right angled triangle
with base of 12 m and an upright of
16 m.
To find the hypotenuse we use Pythagoras' Theorem.
Namely:- Hypotenuse^2 = 12^2 + 16^2
Hypotenuse = √144 + 256
Hypotenuse = √400
Hypotenuse = 20 m
.............
Two equal sides = 20 m
Base = 24 m
Hope this helps :-)