The difference between the length and width of a triangle is 7 units. The perimeter is 50 units. What are the dimensions?
To find the dimensions of the triangle, we need to let x represent the length and y represent the width. Given that the difference between the length and width is 7 units, we have the equation x - y = 7.
The perimeter of a triangle is equal to the sum of its three sides. In this case, the perimeter is given as 50 units. Since the length of the triangle is x and the width is y, the perimeter equation can be written as x + y + z = 50.
However, we don't know the value of the third side (z), so we can't solve this equation just yet. To proceed, we need to eliminate the variable z.
Using the fact that the difference between the length and width is 7 units, we can rewrite the perimeter equation as x + y + (x - y) = 50. Simplifying this equation, we get 2x = 50, which leads to x = 25.
Substituting this value of x back into the equation x - y = 7, we can solve for y. Thus, 25 - y = 7 => y = 18.
Therefore, the dimensions of the triangle are a length of 25 units and a width of 18 units.