1. A rectangular garden has an area of 84 m2and a perimeter of 38 m. Find its length andwidth.2. The length of a rectangular floor is 5 m longerthan its width. The area of the floor is 84 m2.
Answer (1)
Answer: Problem 1 1. Let l be the length and w be the width.2. We have the equations: l * w = 84 and 2l + 2w = 38 .3. Simplifying the perimeter equation gives l + w = 19 .4. Solving for l , we get l = 19 - w .5. Substituting this into the area equation gives (19 - w) * w = 84 .6. Expanding and rearranging, we get w^2 - 19w + 84 = 0 .7. Factoring, we have (w - 12)(w - 7) = 0 .8. Therefore, w = 12 or w = 7 .9. Substituting these values back into l = 19 - w gives us l = 7 or l = 12 . Answer: The garden is 12 meters long and 7 meters wide (or vice versa). Problem 2 1. Let w be the width and l = w + 5 be the length.2. The area equation is l * w = 84 .3. Substituting l = w + 5 gives (w + 5) * w = 84 .4. Expanding and rearranging, we get w^2 + 5w - 84 = 0 .5. Factoring, we have (w + 12)(w - 7) = 0 .6. Since width cannot be negative, we take w = 7 .7. Substituting this into l = w + 5 gives l = 12 . Answer: The floor is 7 meters wide and 12 meters long.
