A rug is shaped like a rectangle whose perimeter is 176 ft. The length is 7 times as long as the width. Find the length and the
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Answer:
Width = 10 inches
Step-by-step explanation:
Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.
We can establish the following values to help us solve for the width of a rectangle:
Perimeter (P) = 68 inches
Length (L) = 14 + W inches
Width (W) = unknown
<h3 /><h3><u>Solve for the Width (W)</u></h3>P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.
Divide both sides by 2:
Substitute the value of the Perimeter and the length (L) into the formula:
Combine like terms on the right-hand side, and simplify the left-hand side of the equation:
Subtract 14 from both sides:
34 - 14 = 14 - 14 + 2W
20 = 2W
Divide both sides by 2 to solve for the width (W):
W = 10 inches
Therefore, the width of the rectangle is 10 inches.
<h3 /><h3><u>Double-check:</u></h3>Verify whether the derived value for the width is correct:
P = 2L + 2W
68 = 2(14 + 10) + 2(10)
68 = 2(34) + 20
68 = 48 + 20
68 = 68 (True statement).
Thus, the length of the rectangle is 34 inches, and the width is 10 inches.
Given:
Total number of students = 10
To find:
How many was can you award first, second, and third place?
Solution:
Total number of students is 10. So, the total possible ways for the first award is 10.
We know that one student can hold only one place. So, after giving the first award, the number of remaining students is 9 and the total possible ways for the second award is 9.
Similarly, the total possible ways for the third award is 8.
Now, the total number of ways to award first, second, and third place is:
Therefore, the total number of ways to award first, second, and third place is 720.