The perimeter of an equilateral triangle is 7 in. more than the perimeter of a square. The side of the triangle is 5 in. longer than the side of the square. Find the length of each side of the triangle. (Note: An equilateral triangle has all sides equal)
Please help!
Let x be the triangle's side length and y be the square's side length.
3x = 4y + 7
x = y + 5
Solve those two simultaneous equations. One way would be to substitute y+5 for x in the first equation. This would give you
3y + 15 = 4y + 7
which leads to y=8 etc.
3
side of the triange is 20 while side of the square is 15
To solve the given problem, we need to set up a system of equations using the information provided.
Let x be the length of each side of the equilateral triangle, and let y be the length of each side of the square.
From the given information, we can set up the following equations:
Equation 1: The perimeter of the equilateral triangle is 7 inches more than the perimeter of the square.
The perimeter of the equilateral triangle is given by 3x, and the perimeter of the square is given by 4y.
Therefore, we have the equation: 3x = 4y + 7.
Equation 2: The side length of the triangle is 5 inches longer than the side length of the square.
The side length of the triangle is x, and the side length of the square is y.
Therefore, we have the equation: x = y + 5.
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution here.
From Equation 2, we have: x = y + 5.
Substitute this value of x into Equation 1:
3(y + 5) = 4y + 7.
Expand and simplify the equation:
3y + 15 = 4y + 7.
Subtract 3y from both sides:
15 = y + 7.
Subtract 7 from both sides:
8 = y.
Therefore, the length of each side of the square is 8 inches.
Substitute this value of y into Equation 2 to find the length of each side of the equilateral triangle:
x = y + 5,
x = 8 + 5,
x = 13.
Therefore, the length of each side of the equilateral triangle is 13 inches.