Question

question the width of a rectangle measures (5h + 2k) centimeters, and its length measures (h + 5k) centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer 6h + 7 12h + 14k 12h + 14 10k + 12h + 2 submit answer

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, the length is \( (h + 5k) \) and the width is \( (5h + 2k) \). So we substitute these into the formula: \( P = 2[(h + 5k)+(5h + 2k)] \).

Step2: Combine like terms inside the parentheses

First, combine the \( h \)-terms and \( k \)-terms inside the brackets: \( (h + 5h)+(5k + 2k)=6h + 7k \). Now the expression becomes \( P = 2(6h + 7k) \).

Step3: Distribute the 2

Using the distributive property \( a(b + c)=ab + ac \), we get \( 2\times6h+2\times7k = 12h + 14k \).

Answer:

\( 12h + 14k \) (corresponding to the option "12h + 14k" among the given choices)