an equilateral triangle has sides of length x+1 cm
The triangle and the square have the same perimeter
A) write down an equation in terms of x that links the perimeter of each shape
b) Solve the equation to find value of x
c) Write down the length of each side of the square
2
Answers
Step-by-step explanation:
Note that each side of the square = 5x + 3
There are four sides, therefore, the perimeter = 4 * (5x + 3) = 20x + 12
2. Similarly, each side of the triangle = 7x - 1
There are three sides, therefore, the perimeter = 3 * (7x - 1) = 21x - 3
3. They have the same perimeter, therefore, the two equations are equal to each other.
Perimeter of triangle = Perimeter of square
21 x - 3 = 20x + 12
4. Solve for x.
Simplify by performing the same operation on both sides of the equation
21 x - 3 = 20x + 12
21 x - 20 x - 3 = 20x + 12 - 20 x
x - 3 = 12
x - 3 + 3 = 12 + 3
x = 15
This is the solution. You have found the x that works in both perimeter expressions.
5. Check the solution. The perimeter lengths should be equal.
f(15) = 20 * x + 12 Be careful to remember order of operations: 20*3 first, then add 12
= 20(15) + 12
= 300 + 12
= 312 linear units
and g(15) = 21 * x - 3 Order of operations again (PEMDAS)
= 21(15) - 3
= 315 - 3
= 312 linear units
Verified. Check!