Help with this problem?

Question

The length of one of the equal legs of an isosceles triangle is 8 cm less than 4 times the length of the base. If the perimter is 29cm, find the length of one of the equal legs.

I know this is probably a A=1/2b * h, but it is not clicking on how to set up the variables for this? Help please!!

Answer 1

You don't need area to get perimeter. Just call the base b, then each leg is 4b - 8

4b - 8 + 4b - 8 + b = 29

You can figure this out - or just wait and someone will tell you the answer

Answer 2

Let x = the length of the base.

Let 4x - 8 = the length of each leg of the isosceles triangle.

Since perimeter is adding up all of the sides, the three sides can be put into an equation in this form: A + B + C = 29

OR

x + (4x-8) +(4x-8) = 29

simplify

9x - 16 = 29

add 16 to both sides (addition property of equality)

9x = 45 divide both sides by 9

x = 5 cm (The length of the base)
4x-8 = 12 cm. (The length of each of the isosceles triangle's legs).

Answer 3

No, this has nothing to do with the area.

Let L be the length of the base in cm. Then one of the equal legs has length 4L - 8. So the other equal leg obviously has this length too.

Thus the total perimeter is L + 2(4L - 8) since we have one side of length L and two sides of length 4L - 8. But we are given the perimeter is 29 cm, so we have
L + 2(4L - 8) = 29
=> L + 8L - 16 = 29
=> 9L = 45
=> L = 5.
So the base is 5 cm and the equal sides have length 4(5) - 8 = 12 cm.

Answer 4

Let x = length of base
Then side = 4x-8
So perimeter = x+2(4x-8) = x+ 8x -16 =9x-16
9x-16 = 29
9x = 45 so x= 5
so side = 4*5-8=12
The triangle has a base = 5 and two sides = 12 each
This gives aperimeter 0f 5+12+12 = 29 as required.

Answer 5

You don't need to use area, just perimeter because you have all the sides and the perimeter..

Let's call the base 'x.'
Each leg is 4x - 8 (8 less... 4 times base)

x + 4x - 8 + 4x - 8 = 29
9x - 16 = 29
9x = 45
x = 5 cm

Now plug this back in your expression for the leg..

4x - 8
4(5) - 8
20 - 8
12 cm

Hope that helps!

Answer 6

you don't even need to use area
perimeter is the sum of all sides
isosceles triangles have two legs of equal length and one base
so one leg is 4x-8 and the base is x
(4x-8) + (4x-8) + x = 29
9x - 16 = 29
9x = 45
x = 5
so then the leg is 4*5-8=12

Answer 7

base=x
leg=4x-8

2leg+base= perimiter
2(4x-8)+x=29
8x-16+x
9x= 45
x= 5

leg=4(5)-8=12

Answer 8

let the lenght of equal sides be x
base=y
perimeter=2x+y=29
x+8=4y
we have to find the value of x
y=29-2x
4y=116-8x
x+8=116-8x
9x=108
x=12