The perimeter of an equlateral triangle is 45 inches. A rectangle whose width is 1/3 its length has a perimeter of 48 inches. Which figure has the longest side? Explain.
What is the length of leg s of the triangle below?
To determine which figure has the longest side, we can solve for the lengths of the sides in each figure and compare them.
Let's start with the equilateral triangle. In an equilateral triangle, all three sides have the same length. Let's denote the length of each side as "s." The perimeter of the triangle is given as 45 inches, so we have:
Perimeter of triangle = 3s = 45 inches
Dividing both sides by 3 gives us the length of each side:
s = 45 inches / 3 = 15 inches
Therefore, each side of the equilateral triangle is 15 inches long.
Now let's move on to the rectangle. We are given that the width is 1/3 its length. Let's denote the length of the rectangle as "l" and the width as "w." The perimeter of the rectangle is given as 48 inches, so we have:
Perimeter of rectangle = 2l + 2w = 48 inches
Since the width is 1/3 the length, we can express the width in terms of the length:
w = (1/3)l
Substituting this expression into the perimeter equation, we get:
2l + 2(1/3)l = 48 inches
Simplifying the equation:
2l + (2/3)l = 48 inches
(6/3)l + (2/3)l = 48 inches
(8/3)l = 48 inches
Now we can solve for the length of the rectangle:
l = (48 inches) / (8/3) = 18 inches
Substituting the length back into the expression for the width:
w = (1/3)(18 inches) = 6 inches
Therefore, the length of the rectangle is 18 inches, and the width is 6 inches.
To determine which figure has the longest side, we compare the lengths of the sides. In the equilateral triangle, each side is 15 inches long. In the rectangle, the longest side is the length, which is 18 inches.
Therefore, the rectangle has the longest side.