each side of an equilateral triangle is 4 cm shorter than twice the length of each side of a square. their perimeter are the same. how long is each side of the triangle?
To find the length of each side of the equilateral triangle, let's break down the information given:
1. Each side of the equilateral triangle is 4 cm shorter than twice the length of each side of the square.
Let's represent the length of each side of the square as "S". So,
Length of each side of the triangle = 2S - 4 cm.
2. The perimeters of the square and the equilateral triangle are the same.
Perimeter of the square = 4 × S
Perimeter of the triangle = 3 × (2S - 4)
Since the perimeters of the square and the triangle are the same, we can set up an equation:
4 × S = 3 × (2S - 4)
Now, let's solve the equation step by step:
4S = 6S - 12 (using distributive property)
4S - 6S = -12 (subtracting 6S from both sides)
-2S = -12 (combining like terms)
S = (-12)/(-2) (dividing both sides by -2)
Simplifying further:
S = 6 cm
Now, we can substitute the value of S back into the equation for the triangle's side length:
Length of each side of the triangle = 2S - 4
Length of each side of the triangle = 2 × 6 - 4
Length of each side of the triangle = 12 - 4
Length of each side of the triangle = 8 cm
Therefore, each side of the equilateral triangle is 8 cm long.
let s = side of triangle
let q = side of square
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s+4 = 2q (equation 1)
perimeters equal so
s+s+s+s = q+q+q+q or
4s = 4q (equation 2)
Solve the two equations simultaneously for s and q.