the base of an isosceles triangle is half as long as side of a square.Each of the legs of triangle is twice as long as a side of the square.How long is each side of the triangle if the sum of the perimeters is 34 m.
Well, well, well. It seems like we've got ourselves a triangle and a square having a little perimeter party, huh? Let's see if we can untangle this one.
Alright, so let's call the side of the square "x". That means the base of the isosceles triangle is half of that, which is just x/2. As for the legs of the triangle, they're twice as long as the side of the square, so they're 2x.
Now, let's add up the perimeters of the square and the triangle. The perimeter of the square is just 4 times the side, so that's 4x. The perimeter of the isosceles triangle is the sum of the base and the two legs, which is x/2 + 2x + 2x = 5x/2.
Now, we're given that the sum of the perimeters is 34m. So we can set up the equation:
4x + 5x/2 = 34
Now, you know I love a little math joke, so let's simplify this equation:
8x/2 + 5x/2 = 34
13x/2 = 34
13x = 68
x = 68/13
So each side of the square is approximately 5.23m (rounded to two decimal places). And since the base of the isosceles triangle is half of that, it's about 2.62m. The legs of the triangle are twice as long as the side of the square, so they're around 10.46m each.
So to answer your question, each side of the isosceles triangle is approximately 2.62m, and the sum of the perimeters is 34m.
Let's denote the side length of the square as "s".
According to the given information, the base of the isosceles triangle is half as long as the side length of the square, which means the base of the triangle is s/2.
Each of the legs of the triangle is twice as long as a side of the square, so each leg of the triangle has a length of 2s.
To find the perimeter of the triangle, we can add up the lengths of all three sides:
s/2 + 2s + 2s = 34
Combining like terms, we get:
s/2 + 4s = 34
Multiply the entire equation by 2 to eliminate the fraction:
s + 8s = 68
Combine like terms again:
9s = 68
Divide both sides by 9 to isolate s:
s = 68/9
s ≈ 7.56
So each side of the square is approximately 7.56 meters long.
Since each leg of the triangle is twice as long as a side of the square, the length of each leg is:
2s ≈ 2(7.56) ≈ 15.12
Therefore, each side of the isosceles triangle is approximately 15.12 meters long.
To solve this problem, let's use variables to represent the side length of the square and the legs of the isosceles triangle.
Let's say that the side length of the square is 's'. Then, the base of the isosceles triangle would be half as long, so it would be 's/2'. Lastly, each of the legs of the triangle would be twice as long as the side of the square, so they would be '2s'.
Now, let's calculate the perimeter of the square. The perimeter of a square is given by the formula: perimeter = 4 * side length. Therefore, the perimeter of the square would be 4s.
Next, let's calculate the perimeter of the isosceles triangle. The perimeter of a triangle is given by the formula: perimeter = sum of all sides. In this case, the sum of all sides would be the base length plus the two leg lengths. So, the perimeter of the isosceles triangle would be (s/2) + 2s + 2s = (s/2) + 4s.
Now, we know that the sum of the perimeters of the square and the isosceles triangle is 34m. Therefore, we can set up the following equation:
4s + (s/2) + 4s = 34
Now, we can solve this equation for 's' to find the length of each side of the square:
8.5s = 34 (combining like terms)
s = 4
So, the side length of the square is 4m.
Now, we can substitute this value back into our expressions to find the length of each side of the isosceles triangle:
Base: s/2 = 4/2 = 2m
Legs: 2s = 2 * 4 = 8m
Therefore, each side of the isosceles triangle is 2m and each leg is 8m.
base = s/2
leg = 2s
s/2 + 2*2s + 4s = 34
Now solve for s, and then the triangle's sides.