Question

The area of an isosceles triangle is 12 CM square. If one of its equal sides is 5 cm,find its base.​

Answer 1

Answer:

 8 cm or 6 cm could be the bases

Step-by-step explanation:

Let half of the base be 'b'

Hypotenuse of the triangle =   5 cm

Base= b     Height=h

Area of a triangle= 1/2*b*h

Here, the entire base is 2b

Therefore, 1/2*2b*h=12cm^2

b*h=12 cm^2

To proceed further,

Let 'h' be 12/b cm

Pythagoras property

a^2+b^2=c^2

b^2+(12/b)^2= 5^2

b^2+(144/b^2)=25

(b^4+144)/b^2=25

b^4+144=25b^2

b^4-25b^2+144=0

By spiting the middle term,

b^4-9b^2-16b^2+144

b^2(b^2-9)-16(b^2-9)

(b^2-16)(b^2-9)=0

Either,(b^2-16)=0 or (b^2-9)=0

Either b^2=16 or (b^2=9)

Therefore, b can be either 4 or 3

As 2b is the base, it can be either 8 cm or 6 cm

If 8 cm is the base, then 3 cm will the height.

If 6 cm is the base, then 4 cm  will be the height.

Hope it helps you!!!