Each of the equal sides of an isosceles triangle is 7 cm longer than the other side. The perimeter is 89 cm. What is the
length of each of the sides of the triangle?
To find the length of each side of the isosceles triangle, we can set up an equation using the given information.
Let's denote the length of the equal sides as x, and the length of the other side as y.
According to the problem, each of the equal sides is 7 cm longer than the other side, so we can write the equation: x = y + 7.
The perimeter of a triangle is the sum of its three sides. In this case, we have two equal sides and one different side. Thus, the equation for the perimeter is: 2x + y = 89.
To solve this system of equations, we can substitute the value of x from the first equation into the second equation.
Substituting x = y + 7 into 2x + y = 89, we get: 2(y + 7) + y = 89.
Simplifying the equation gives us: 2y + 14 + y = 89.
Combining like terms, we have: 3y + 14 = 89.
Subtracting 14 from both sides, we get: 3y = 75.
Finally, dividing both sides by 3, we find: y = 25.
Now that we know the value of y, we can substitute it back into the first equation to find x.
Substituting y = 25 into x = y + 7, we get: x = 25 + 7 = 32.
Therefore, the length of each of the equal sides of the triangle is 32 cm, and the length of the other side is 25 cm.