rectangular room is
3
3
times as long as it is wide, and its perimeter is
40
40
meters. Find the dimension of the room.
The length is : meters and the width is
L = 3W
2L + 2W = 40
Substitute 3W for L in the second equation and solve for W. Insert that value into the first equation to solve for L. Check by putting both values into the second equation.
Let's solve this problem step by step:
Step 1: Let's assume the width of the room as "x" meters.
Step 2: According to the given information, the length of the room is 3 times its width. So, the length would be 3x meters.
Step 3: The formula to calculate the perimeter of a rectangular room is given by P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Step 4: Substituting the values, we can write the equation as 40 = 2(3x + x).
Step 5: Simplifying the equation, we get 40 = 2(4x).
Step 6: Further simplifying, we have 40 = 8x.
Step 7: Dividing both sides of the equation by 8, we find x = 5.
Step 8: Now that we have the width, we can find the length by multiplying 3 with the width. Thus, the length is 3 * 5 = 15 meters.
So, the dimension of the room is: Length = 15 meters and Width = 5 meters.