a carpet is on the floor 8m by 5m . area of border on the carpet is 12m squared.find width and length of carpet. can we use heron'S FORMULA in this?
heron's formula is for triangles.
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To find the width and length of the carpet, we need to subtract the area of the border from the total area of the carpet. Let's break down the steps:
1. Find the total area of the carpet by multiplying the length by the width:
Area of the carpet = Length x Width = 8m x 5m = 40m²
2. Subtract the area of the border from the total area of the carpet to find the area of the inner part:
Area of the inner part = Total area of the carpet - Area of the border = 40m² - 12m² = 28m²
3. Now, we have the area of the inner part, but we need to find the width and length of the carpet. Since we know the area, we can use the fact that the width times the length is equal to the area:
Width x Length = Area of the inner part = 28m²
4. This equation has two variables (width and length), so we cannot directly solve for them. Heron's Formula, which is used to find the area of a triangle, is not applicable in this case since we are dealing with a rectangle rather than a triangle.
5. However, we can deduce the possible combinations of width and length that satisfy the equation Width x Length = 28m². These combinations are:
- Width = 1m, Length = 28m
- Width = 2m, Length = 14m
- Width = 4m, Length = 7m
- Width = 7m, Length = 4m
- Width = 14m, Length = 2m
- Width = 28m, Length = 1m
6. Therefore, the possible dimensions of the carpet are: 1m x 28m, 2m x 14m, 4m x 7m, 7m x 4m, 14m x 2m, or 28m x 1m.
Remember that the area of the border does not affect the possible dimensions of the carpet but helps determine the area of the inner part.