A rectangular field measures 150ft by 80ft. Part of the lawn is torn up to install a walk of uniform width around it. The area of the new field is one-half the area of the old. How wide is the walk?

Question

Mathematics

Cristopher Watson

30 April, 13:37

A rectangular field measures 150ft by 80ft. Part of the lawn is torn up to install a walk of uniform width around it. The area of the new field is one-half the area of the old. How wide is the walk?

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Demetrius Ho · Answer 1

Half the area is 6000.

let x be the width of the walk so the inner rectangle has a length of 150-2x and width 80-2x and hence its area is (150-2x) (80-2x) which is equal to 6000.

so now we have an equation in terms of x which reduces to a quadratic and we solve for x