A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width - Maths - Area Theorems

Question

A rectangular garden 10 m by 16 m is to be surrounded by a concrete
walk of uniform width Given that the area of the walk is 120 square
metres, assuming the width of the walk to be x, form an equation in
x and solve it to find the value of x

Gursheen Kaur · Accepted Answer

Solution)
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Let PQRS be the rectangular garden
We have, length of the garden PQRS = 16 mbreadth of the garden PQRS = 10 mNow, area of the garden PQRS = 16 × 10 = 160 m2Let x m be the uniform width of concrete walk that is built around the garden
Now, length of the rectangle ABCD = 16+2x mbreadth of the rectangle ABCD = 10+2x mnow, area of ABCD = length × breadth = 16+2x 10+2x = 4x+8x+5 = 4x2+13x+40Now, area of the concrete walk = area of ABCD - area of PQRS⇒120 = 4x2+13x+40 - 160⇒4x2+13x+40 = 280⇒x2+13x+40 = 70⇒x2 + 13x- 30 = 0⇒x2  + 15x - 2x - 30 = 0⇒xx+15 - 2x + 15 = 0⇒x - 2x + 15 = 0⇒x - 2 = 0  or  x + 15 = 0⇒x = 2   or   x = -15   rejectedSo, uniform width of the concrete walk = 2 m

A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x