each side of equilateral triangle is 5 cm shorter than the side of square. the sum of the perimeters of the two figures is 251 cm. how long is each side of the triangle?
solution pls.
I will set up your definitions
let each side of the square be x
then each side of the triangle is x-5
"the sum of the perimeters of the two figures is 251 cm"
translate this into your equation, then solve for x
Replace you x value in the definitions.
let me know what you got
is the answer is x = 128
not very likely!
that would make the perimeter of the square alone equal to 512
wouldn't your equation have been
4x + 3(x-5) = 251 ??
I get x = 38
(which meets all the conditions)
To find the length of each side of the equilateral triangle, let's assume the side length of the square is "x" cm.
According to the problem, each side of the equilateral triangle is 5 cm shorter than the side of the square. Therefore, the side length of the equilateral triangle can be represented as "x - 5" cm.
Now, we need to set up the equation based on the given information. The sum of the perimeters of the square and the equilateral triangle is 251 cm. The perimeter of the square is 4 times the side length, and the perimeter of the equilateral triangle is 3 times the side length. So, we can write the equation as:
4x + 3(x - 5) = 251
Now, let's solve this equation to find the value of "x" and then the length of each side of the equilateral triangle.
4x + 3x - 15 = 251
7x - 15 = 251
7x = 251 + 15
7x = 266
x = 266/7
x ≈ 38
So, the side length of the square is approximately 38 cm. Now, we can find the side length of the equilateral triangle by subtracting 5 from this value:
x - 5 ≈ 38 - 5 ≈ 33
Therefore, each side of the equilateral triangle is approximately 33 cm long.