14x8 cm? That must be the lawn for a Polly Pocket house!
If the width of the path is x, then
(14+2x)(8+2x) - 14*8 = 48
x = 1
A rectangular lawn measures 14cm by 8cm.it is surrounded by a path of uniform width.If the area of the path is 48cm²,find it's width
2 answers
suspect you mean meters not centimeters
length = 14+ 2 w
width = 8 +2 w
total area to outside of path = (8+ 2w )(14 + 2w) = 4 (4+w)(7+w)
= 4 ( 28 +11 w + w^2)
area inside path = 14*8
so
48 = 4 ( 28 +11 w + w^2) - 14 * 8
12 = ( 28 +11 w + w^2) - 28
w^2 + 11 w - 12 = 0
(w+12)(w-1) = 0
w = 1
length = 14+ 2 w
width = 8 +2 w
total area to outside of path = (8+ 2w )(14 + 2w) = 4 (4+w)(7+w)
= 4 ( 28 +11 w + w^2)
area inside path = 14*8
so
48 = 4 ( 28 +11 w + w^2) - 14 * 8
12 = ( 28 +11 w + w^2) - 28
w^2 + 11 w - 12 = 0
(w+12)(w-1) = 0
w = 1
2 answers