Question 1020860: The perimeter of an equilateral triangle is 77 inches more than the perimeter of a square, and the side of the triangle is 55 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length.
Answer by ikleyn(52781)   (Show Source):
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The perimeter of an equilateral triangle is 77 inches more than the perimeter of a square, and the side of the triangle is 55 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length.
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From the condition, you have this system of equations:
3t = 4s + 77, (1)
t = s + 55, (2)
where t = the length of the side of the triangle, s is that of square.
To solve it, simply substitute the expression t = s + 5 of (2) into equation (1). You will get an equation for one single unknown
3*(s+55) = 4s + 77,
which is easy to solve:
s = 165 - 77 = 88.
Then t = s + 55 = 88 + 55 = 143.
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