Question

the legs of a right triangle are in the ratio 3:4 and its area is 1014 CM square find its hypotenuse

Answer 1

I didn't understood from where did your triangle got legs

Answer 2

Let the 2 sides of the triangle be 3x and 4x.
area of a triangle = 1/2*base*height
1014 = 1/2*3x*4x
1014 = 3x*2x
1014 = 6xsquare
1014/6 = x square
169 = x square
$\sqrt{169}$
There fore,
x = 13 cm
thus,
3x = 3*13 = 39
4x = 4*13 = 52
let hypotenuse be 'a' (pythogorus theorem)
(a)2 = (39)2 + (52)2
a =
$\sqrt{1521 + 2704}$
a =
$\sqrt{2743}$

a = 52.374(approx)

Hope it helps you...