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?

answered.

90 To solve this problem, we can set up equations using the given information and then solve them simultaneously.

Let's say that the length of the two equal sides of the triangle is 'x' cm.

According to the problem, the remaining side is one third as long as each of the other sides. So, the length of the remaining side is (1/3)x cm.

The perimeter of a triangle is the sum of the lengths of all three sides.

Therefore, we can set up the equation: x + x + (1/3)x = 315.

Combining like terms, we have: (2 + 1/3)x = 315.

To simplify the equation, we can multiply both sides by the least common multiple of 2 and 1/3, which is 6.

6 * (2 + 1/3)x = 6 * 315.

This simplifies to: (12 + 2)x = 1890.

Further simplifying, we have: 14x = 1890.

Now, let's solve for x by dividing both sides of the equation by 14.

(14x)/14 = 1890/14,

x = 135.

Therefore, the length of each of the equal sides of the triangle is 135 cm.

And the length of the remaining side is (1/3)x = (1/3) * 135 = 45 cm.