A rectangular garden has a perimeter of 28 m and an area of 45 m². What is the ratio of the shorter side to the longer side?
The ratio of the shorter side to the longer side is 2 to 3.
To solve for the dimensions of the rectangular garden, we need to use the perimeter and area formulas. The perimeter is given as 28 m, and the area is 45 m². By setting up the equations for the length (l) and width (w), we find that the dimensions are 6 m and 9 m, respectively, leading to a ratio of 2:3 when comparing the shorter side to the longer side.
This ratio is derived from the dimensions of the garden, which are 6 m (shorter side) and 9 m (longer side). The calculation is straightforward: 6/9 simplifies to 2/3, confirming that this is the correct ratio of the shorter side to the longer side of the rectangular garden.
This ratio does not accurately reflect the dimensions of the garden. If we assume a shorter side of 3 units, the corresponding longer side would need to be 5 units in a 3:5 ratio, which would yield an area of 15 m² (3 * 5), contradicting the given area of 45 m². Therefore, this option is incorrect.
Similar to option B, a 4:5 ratio implies that if the shorter side is 4 units, the longer side would be 5 units, producing an area of 20 m² (4 * 5). This also does not match the required area of 45 m², making this choice invalid.
This ratio incorrectly suggests a shorter side of 5 units and a longer side of 9 units, which would yield an area of only 45 m² (5 * 9). While this matches the area, it reverses the context of shorter and longer sides, and thus does not reflect the correct ratio of shorter to longer.
The dimensions of the rectangular garden yield a ratio of the shorter side to the longer side as 2 to 3. Through the calculations involving perimeter and area, we confirmed that the shorter side measures 6 m and the longer side measures 9 m, establishing the correct ratio. All other choices fail to provide valid dimensions or misrepresent the relationship between the sides.
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