math has me in an up roar?

Question

The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 time the length of the base. If the perimeter is 29 cm find the lenght of one of the eqaul legs.

Would I start with 4x-8=29

and woul the answer be 4,5,11 or 12cm???

Answer 1

length of legs = 4x-8
base =x

so to find perimeter, add up the sides, right?

x + (4x-8) + (4x-8) = 29
9x - 16 = 29
9x = 45
x=5, but x is the base, not a leg

leg = 4x -8 = 4(5) -8 = 12 cm

Answer 2

Start by making variables for the quantities discussed in the problem. That always helps the English-to-algebra translation.

So:

Let "b" be the "the length of the base."
Let "x" be "the length of one of the equal legs."

Also, since it's an isosceles triangle, the length of the OTHER leg is also "x". That will help us later.

Now for the translation:

"The length of one of the equal legs..."
x

"...is 8 cm less than 4 time the length of the base."
= 4b - 8

So, first equation (from Sentence 1) is:
x = 4b - 8

Second sentence:

"...the perimeter is 29..."
x + x + b = 29
or:
2x + b = 29

So now we have two equations:

x = 4b - 8
2x + b = 29

You want to find "the length of one of the equal legs," which we've defined as x. So now the thing to do is to manipulate the two equations above until you get rid of the "b" and just have an equation with "x" in it.

Best way to do that is:
1. Solve 1st equation for b (so you get "b = something")
2. Substitute the "something" into the 2nd equation, wherever "b" appears.
That should leave you with an equation that only has "x" in it. Then you just solve for "x".

Answer 3

If x is the length of the base, then each of the equal sides is (4x-8).
Perimeter = sum of lengths of all 3 sides
= sum(2 equal sides) + base
= 2(4x - 8) + x = 29
8x - 16 + x= 29
9x = 45
x = 5 = length of base
and length of each equal side = 4x - 8 = 20 - 8 = 12

(Check: 12 + 12 + 5 = 29 )

Answer 4

Let L = length of leg
B = length of base

One of the legs is equal to 8 less than 4 times the base:
L= 4B-8

The perimeter, P, is 29
P = L + L + B

Substitute:
P = (4B-8) + (4B-8) + B = 8B + B - 16 = 29
9B-16 = 29
9B = 45
B = 5

L = 4B-8 = 4·5 - 8 = 20 - 8 = 12

Check:
P = 29 = 12 + 12 + 5 = 29
valid

So one of the equal legs is 12 cm long