One side of triangle is half the longest side. the third side is 7 feet less than the longest side. the perimeter is 43. find all three sides.

If x is the longest side, and y is half that length, you would have the equation

2y = x

If z is 7 less than x then that equation would look like

X = z +7

The perimeter is the sum of all the sides

P = x + y + z = 43

Now by using all three equations, we can find the value of each variable by plugging into the equations.
First, let's start by changing the first two equations to compare the values of z and y to x.

Y = x/2
Z = x - 7

Now we can use these new equations to plug into the perimeter equation and find the value of x.

43 = x + y + z Plug in your variables
43 = x + x/2 + x-7 Add 7 to both sides
50 = x + x/2 + x Multiply both sides by 2 to get rid of the fraction
100 = 2x + x + 2x Add all your x's together
100 = 5x Divide both sides by 5

X = 20

No we can use the value of x to find the values of y and z by plugging into the two equations before.

2y = 20
Y = 10

Z = 20 - 7
Z = 13

Therefore, the lengths of the sides are 20, 10, and 13