Help me with my equation math homework?

Question

Homework is to change this into a 1 step equation. (I can solve)

The base of an isocles triangle is 5 meters less than 4 times the length of a side. The perimeter is 67 meters. Find the length of each side and the base.

I really don't understand this stuff, so if someone could help that would be great.

Answer 1

An iscoceles triangel has two sides of equal length and two equal angles. Let the sides be B (the base), S, and S.

"The base is 5 meters less than 4 times the length of a side"

B = 4S - 5

"The perimeter is 67 meters."

B + S + S = 67

You now have two equations and two unknowns. We'll use the first equation as a substitution into the second:

( 4S - 5 ) + S + S = 67

6S - 5= 67

6S = 72

S = 72 / 6 = 12

Then

B = 4S - 5 = 4 ( 12 ) - 5 = 43

Answer 2

OK

An isocles triangle, by defintion, has the two sides equal. SO

b + 5 = 4s, (add 5 to the base to make it equal to 4s)

and 2s + b = 67 (perimeter is s+s+b)

b-4s = -5
b+2s = 67; subtract the bottom from the top and the b's go away

-6s = -72
s = 12

So the sides are each 12m.

P = b + 2(12)
67 = b+24
43 = b

So the base is 43m.

Final check
b + 5 = 4s
43+5 = 4(12)
48 = 48 YES!!

Hope that help!

Answer 3

let b = length of base and s = length of a side
perimeter: b + 2s = 67
1st part: b = 4s - 5

substitute b in 1st part into perimeter
(4s - 5) + 2s = 67
6s = 72
s = 12

b = 4(12) - 5
b = 43

each side = 12 meters
base = 43 meters

Answer 4

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