Katie H. answered • 01/07/21
Designer & Youth Educator - Art and Academics tutoring
Let's break down these sentences! We can call the largest side L, the middle side M, and the smallest side S to keep things easy.
The perimeter of the triangle is 43cm.
That can be written as: L + M + S = 43
The largest side is 4 times the smallest side.
That can be written as: L = 4*S, or L = 4S
The middle side is 8 more than twice the smallest side.
Start with "twice the smallest side" - this can be written as 2S
This middle side is 8 more than that, so we can write: M = 2S + 8
Now we have L and M defined in terms of S. Let's go back to the original equation for the perimeter and plug these in.
L + M + S = 43
4S + (2S + 8) + S = 43
combine the terms of S (4S, 2S, S)
7S + 8 = 43
subtract 8 from each side
7S = 35
divide each side by 7
S= 5 The length of the smallest side is 5cm.
If you want to double check your answer, you can replace S with 5 in the perimeter equation and see if it checks out.
L + M + S = 43
4S + (2S + 8) + S = 43
7S + 8 = 43
7(5) + 8 = 43?
43 = 43 correct!
