The length of one of the equal legs of an isosceles triangle is 3inches less than twice the length of the base. If the perimeter is 29 inches , what is the length of each of the sides?
2(2 b - 3) + b = 29 ... 5 b - 6 = 29
L = 2b - 3
To find the lengths of the sides of an isosceles triangle, we need to set up an equation based on the given information.
Let's assume that the length of one of the equal legs is x inches.
According to the given information, the length of the base is 3 inches more than half of the length of one of the equal legs. So, the length of the base is (1/2)x + 3 inches.
Since the triangle is isosceles, we know that the lengths of the two equal legs are the same. Therefore, the total length of the equal legs is 2x inches.
Finally, using the perimeter formula for a triangle which is the sum of the lengths of all three sides, we can set up the equation:
x + (1/2)x + 3 + (1/2)x + 3 = 29
Now, let's solve this equation to find the value of x:
2x + x/2 + x/2 + 6 = 29
(4x + x + x + 12)/2 = 29
6x + 12 = 58
6x = 46
x = 46/6
x ≈ 7.67
So, the length of one of the equal legs is approximately 7.67 inches.
To find the length of each side of the triangle, we can substitute this value back into our expressions:
Length of one of the equal legs = x ≈ 7.67 inches
Length of the base = (1/2)x + 3 ≈ (1/2)(7.67) + 3 ≈ 6.84 inches
Therefore, each side of the triangle has a length of approximately 7.67 inches for the equal legs and 6.84 inches for the base.
Let's assume that the length of the base of the isosceles triangle is 'x' inches.
According to the given information, one of the equal legs is 3 inches less than twice the length of the base. So, the length of the equal legs can be expressed as 2x - 3 inches.
The perimeter of a triangle is the sum of the lengths of all sides. In this case, the perimeter is 29 inches. Since the isosceles triangle has two equal legs, the perimeter can be calculated as follows:
Perimeter = base length + equal leg length + equal leg length
Using the lengths mentioned above, we can write the equation as:
29 = x + (2x - 3) + (2x - 3)
Simplifying the equation:
29 = x + 2x - 3 + 2x - 3
29 = 5x - 6
Adding 6 to both sides:
29 + 6 = 5x
35 = 5x
Dividing both sides by 5:
35/5 = x
7 = x
So, the length of the base is 7 inches.
Now, we can substitute the value of 'x' into 2x - 3 to find the length of one of the equal legs:
Equal leg length = 2x - 3 = 2(7) - 3 = 14 - 3 = 11 inches
Therefore, each of the sides of the isosceles triangle has a length of 7 inches for the base and 11 inches for the equal legs.