Answer to Question #322470 in Linear Algebra for Kenth Smith

Question

A man wishes to fence in a rectangular lot. If he uses material costing P17/meter for the front of the lot and material costing P14/meter for the other three sides, the fence will cost P8,900. If he uses the cheaper material for all four sides, the fence will cost P8,540. Find the dimensions of the lot.

Answer 1

AD - P17/meter

AB,BC,CD - P14/meter

If AD "x" meters, AB+BC+CD "y" meters

• 17x+14y=8900
• 14(x+y) =8540

• 17x+14y=8900
• -14x-14y=-8540

Then 3x=360

x = 120 meters

14(x+y)= 8540

x+y=610

then 120+y=610

y=490

If ABCD - rectangle, then AB=CD, BC=AD

AD=120 meters, BC=120 meters

AB+BC+CD =490

AB+120+CD =490

AB=CD=490/2=185

Answer: Dimensions of the lot 120 and 185 meters