Two sides of a triangle have the same length. The remaining side is one third as long as each of the other sides. If the perimeter of the triangle is 315 cm, what is the length of each side?
x+x+1/3(x)=315
Answer
The two even sides are 135
And the shorter side is 45
Let's assume that the two sides with the same length are represented by 'x' and the remaining side is represented by '1/3x'.
To find the perimeter of the triangle, you need to add up the lengths of all three sides. The formula for the perimeter of a triangle is:
Perimeter = Side 1 + Side 2 + Side 3
In this case, we know that the perimeter of the triangle is 315 cm. So we can write the equation as:
315 = x + x + 1/3x
Now, let's simplify the equation:
315 = 2x + 1/3x
To make it easier to solve the equation, let's get rid of fractions. Multiply everything by the LCD (Least Common Denominator) of 3, which is 3:
3 * 315 = 3 * (2x + 1/3x)
945 = 6x + x
Combine like terms:
945 = 7x
Now, divide both sides of the equation by 7 to solve for 'x':
945 / 7 = x
135 = x
So, we have found that the length of each of the two sides with the same length is 135 cm.
Now, let's find the length of the remaining side.
We know that the remaining side is one-third as long as each of the other sides. So, we multiply 'x' by 1/3 to find its length:
(1/3) * 135 = 45
Therefore, the length of each side is 135 cm and the length of the remaining side is 45 cm.