# If isosceles triangle has a perimeter of 82 cm. And the lengths of the legs are (5x-14) and (3x+2) then what is the length of the base?

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In an isosceles triangle, two legs are equal in length and the third leg is called the base.

In this case, your two legs have the lengths (5x-14) and (3x+2). We can find out the lengths of these legs because we know they are equal. So we set up the equation

5x-14 = 3x+2

Subtract 3x from each side to get

2x-14 = 2

Add 14 to each side to get

2x = 16

Divide both sides by 2 to get

x = 8

So now to find the lengths of the legs, plug 8 back in for x.

5x-14 becomes (5*8)-14 which is 40-14 which is 26.

So your legs are 26 cm each, 52 cm total.

If your perimeter is 82 cm, then you subtract the length of the legs from that to find the base.

82-52 = 30

The base of the triangle is 30 cm

The lengths of the isosceles sides: 5x-14 and 3x+2.Therefore, the base of the triangle is given by: length of the base = perimeter-(5x-14+3x+2)=82-7x+12 = **94-8x**........(1)

But the isosceles sides means equal sides. So,

5x-14=3x+2 or

5x-3x=2+14=16

2x=16. Therefore,

x=16/2=8.......................(2)

Now substituting x=8 in (1), we get the lenth of the base=

= 94-8x=94-8*8=94-64=30cm

So, the base of the isosceles triangle is 30cm.