there is a path of uniform width outside and around a rectangle garden of discussion 30m×20m area of path I'd 104m square .what is the width of the garden?
kvnmurty:
qn is to find the width of the path around the garden... not width of the garden..
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See the diagram enclosed of the garden and the path around it.
Let the park be of size: L = 30 m. B = 20 m.
Let the width of the path be w meters.
Area of the path = 2 * (L+2w) *w + 2 * (B+2w)* w - 4 w * w
We subtract 4 w² because the 4 corner squares are added twice in the calculation of the first two terms.
So 104 m² = 2 (30+2w) w + 2 *(20+2w)w - 4 w²
104 = 100 w + 4 w²
w² + 25 w - 26 = 0
(w - 1)(w + 26) = 0
w = 1 m (ignore negative value.
Width of the path = w = 1 m.
===================== another way
104 = path area = (30+2 w) * (20 + 2 w) - 30 * 20
= 600 + 100 w + 4 w² - 600
26 = 25 w + w²
So w = 1 m.
Let the park be of size: L = 30 m. B = 20 m.
Let the width of the path be w meters.
Area of the path = 2 * (L+2w) *w + 2 * (B+2w)* w - 4 w * w
We subtract 4 w² because the 4 corner squares are added twice in the calculation of the first two terms.
So 104 m² = 2 (30+2w) w + 2 *(20+2w)w - 4 w²
104 = 100 w + 4 w²
w² + 25 w - 26 = 0
(w - 1)(w + 26) = 0
w = 1 m (ignore negative value.
Width of the path = w = 1 m.
===================== another way
104 = path area = (30+2 w) * (20 + 2 w) - 30 * 20
= 600 + 100 w + 4 w² - 600
26 = 25 w + w²
So w = 1 m.
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