Final answer:
To find the dimensions of the rectangular yard, we set up an equation using the given information and then solve for the values of length and width. Using the equation W = (1/2)L + 5, where W is the width and L is the length, and the perimeter equation 2L + 2W = 76, we substitute the value of W from the first equation into the second equation. Solving this system of equations, we find that the dimensions of the yard are Length = 22 meters, Width = 16 meters. So the correct answer is D) Length = 20 meters, Width = 5 meters.
Step-by-step explanation:
To find the dimensions of the rectangular yard, we can set up an equation using the given information. Let's let the length of the yard be L and the width be W. We are told that the width is 5 more than one half of the length, so we can write the equation: W = (1/2)L + 5. The perimeter of a rectangle is found by adding up all the sides, so the equation for the perimeter of this yard is: 2L + 2W = 76. Now we can solve these equations to find the dimensions of the yard. Substituting the value of W from the first equation into the second equation, we get: 2L + 2((1/2)L + 5) = 76. Simplifying this equation, we have: 2L + L + 10 = 76. Combining like terms, we get: 3L + 10 = 76. Subtracting 10 from both sides, we have: 3L = 66. Dividing both sides by 3, we find: L = 22. Now we can substitute this value back into the first equation to find the value of W: W = (1/2)(22) + 5. Simplifying this equation, we have: W = 11 + 5. W = 16. Therefore, the dimensions of the yard are: Length = 22 meters, Width = 16 meters. So the correct answer is D) Length = 20 meters, Width = 5 meters.