Two perpendicular cross roads of equal width run through the middle of a rectangular field of length 80 m and breadth 60 m. If the area of the cross roads is 675 square meters, then the width of each road is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5 m
Each road runs the full length or breadth of the field, but the two roads share a square of side \(x\) where they cross. Adding the two roads counts that square twice, so it is taken away once.
Area of the cross roads \(=80x+60x-x^2=140x-x^2\)
\(140x-x^2=675\), so \(x^2-140x+675=0\)
\((x-5)(x-135)=0\), so \(x=5\) or \(x=135\)
A road 135 m wide cannot fit in a field 60 m broad, so the width is 5 m
Shortcut: Test the options in \(140x-x^2\): for \(x=5\), \(700-25=675\), which is the given area.