an equilateral triangle has its perimeter equal to the area of a square if the perimeter of a triangle is divided by half the area of a square it will result to 2 what is the area of a square?
An equilateral triangle and a square have equal perimeters. If the area of the square is 45cm^2, what is the area of the triangle?
The area of the triangle is 20(sqrt3) square centimeters. Here’s my solution path:
Let t be the length of each side of the equilateral triangle. Then the perimeter of the triangle is 3t; and the area of the triangle is (sqrt3)(t^2)/4.
If we can find the value of t^2, finding the area will be easy.
Let s be the length of each side of the square. Then the perimeter of the square is 4s; and the area of the square is s^2 =45 (ignoring units for the moment.)
The equilateral triangle and the square have equal perimeters so 3t = 4s, which leads to 9t^2 = 16s^2. And so t^2 = (16/9)s^2 = (16/9)(45)= 80.
The area of the equilateral triangle is (sqrt3)(80)/4 = 20(sqrt3) square centimeters.
Answers & Comments
Answer:
An equilateral triangle and a square have equal perimeters. If the area of the square is 45cm^2, what is the area of the triangle?
The area of the triangle is 20(sqrt3) square centimeters. Here’s my solution path:
Let t be the length of each side of the equilateral triangle. Then the perimeter of the triangle is 3t; and the area of the triangle is (sqrt3)(t^2)/4.
If we can find the value of t^2, finding the area will be easy.
Let s be the length of each side of the square. Then the perimeter of the square is 4s; and the area of the square is s^2 =45 (ignoring units for the moment.)
The equilateral triangle and the square have equal perimeters so 3t = 4s, which leads to 9t^2 = 16s^2. And so t^2 = (16/9)s^2 = (16/9)(45)= 80.
The area of the equilateral triangle is (sqrt3)(80)/4 = 20(sqrt3) square centimeters.
Explanation:
hope its help