Question

The area of an isosceles triangle is 12 m square. if one of its equal side is 5 M. Find it base.

Answer 1

Let the base be b cms.

Then the semi-perimeter s = (b+5+5)/2 = (b+10)/2.

By Heron's formula, area of the triangle = rt {s(s-a)(s-b)(s-c)}

i.e., 12 = rt{(b+10)/2 ((b+10)/2 -b))((b+10)/2 -5)((b+10)/2 -5))

Squaring, 144 = (b+10)/2 (10-b)/2 (b/2)(b/2)

Simplifying we get b^4 -100b^2 + 2304 = 0 which yields b = 6 or 8.

Hence the length of the base is 6 cms or 8 cms

Answer 2

Following are the available values:

Base: ?

Area: 12 cm sq

side 1: 5 cm

The formula of area is :

1/2 X base X height

- let the base be 2b and height be h.

- bXh= 12

- h= 12/b

- use Pythagoras theorem:

b²+h²= 5²

so b²+ 12²/b²= 25

so next your equation will be: b( power 4) - 25b²+144=0

So next (b + 4)(b – 4)(b + 3)(b – 3) = 0

Neglecting the negative values, b could be 3 giving h = 4

or b could be 4 giving h = 3

This means the whole base could be 6 and the height is 4

OR the whole base could be 8 and the height is 3

PLZZZ!!!