The base of an isosceles triangle is four less than the sum of the lengths of the legs. If the perimeter of the triangle is 44, find the length of the three sides of the triangle.[ Only an algebraic solution will be accepted ]
let each of the equal sides be
let the base by y
then 2x + y = 44
y = 44-2x
So the base is 44 - 2x
"The base of an isosceles triangle is four less than the sum of the lengths of the legs" ---> 44 -2x = 2x-4
44 - 2x = 2x - 4
-4x = -48
x = 12
Each of the two legs is 12, and the base is 44-24 = 20
To solve this problem algebraically, we need to set up equations based on the given information.
Let x be the length of each leg of the isosceles triangle.
We know that the base of the triangle is four less than the sum of the lengths of the legs. So the base would be (2x - 4).
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, it is given as 44. Therefore, we can write the equation:
2x + (2x - 4) + (2x - 4) = 44
Now we can solve this equation for x.
2x + 2x - 4 + 2x - 4 = 44
6x - 8 = 44
6x = 52
x = 52/6
x = 8.6667 (rounded to four decimal places)
Now we have found the value of x, which represents the length of each leg of the isosceles triangle.
To find the lengths of all three sides, we substitute x back into the expressions for the base and legs:
Base = 2x - 4 = 2(8.6667) - 4 = 13.3333 (rounded to four decimal places)
Leg 1 = x = 8.6667 (rounded to four decimal places)
Leg 2 = x = 8.6667 (rounded to four decimal places)
Therefore, the length of the three sides of the triangle are approximately:
Base = 13.3333
Leg 1 = 8.6667
Leg 2 = 8.6667