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Area of Plane Figure and Solving Unknown Variable

The given problem is an application of solving area of the plane figure in real life situation. You will apply your basic knowledge in mathematics and geometry especially in solving area of plane figure and how many items can be occupied in the space provided presented in algebraic expression. Also solving unknown variables.

The given problem is "A rectangular garden is 30 ft by 40 ft long. A covered walk with a uniform width that surrounds it has an area of 296 sq. ft. Find the width of the covered walk".

Step-by-step Solution and Discussion

How to find the area of a rectangle? Area of a rectangle is the space occupied by the shape express in square units. Finding area is the of the product of length and width (A = lw).

Step 1: Identify all the given in the problem

rectangular garden is 30 ft by 40 ft

an area of 296 sq. ft, covered walk

Step 2: Identify what is being ask

Find the width of the covered walk.

Step 3: Make a mathematical equation

let x for the width of the covered walk

A = 296 ft² → area of covered walk

→ 296 = [4(x)² + 2(l-2x)(x) + 2(w-2x)(x)]

Step 4: Solve for x

296 = [4(x)² + 2(l-2x)(x) + 2(w-2x)(x)]

when l = 40 and w = 30

296 = 4(x²) + 2(40-2x)(x) + 2(30-2x)(x)

296 = 4x² + 80x - 4x² + 60x - 4x²

296 = 80x - 4x² + 60x

4x² - 140x + 296 = 0

4x² - 140x + 296 = 0 solve for x using Quadratic Equation ½[-b±√(b²-4ac)], the the value of x is 2.26 ft.

Step 5: Checking

When x = 2.26 ft

Area of covered walk = 296

296 = [4(2.26)² + 2(40-2(2.26)(2.26) + 2(30-2(2.26)(2.26)]

296 = [20.4304 + 160.3696 + 115.1696]

296 = 295.9696

296 = 296 ft² ✓

Final Answer

2.26 ft

Tips in Solving Math problems

• Apply your knowledge in previous topics.
• Don't forget the units of the problem, convert the unit first if necessary before you jump in the solution.
• Identify what formula is needed
• Create mathematical equation, then solve
• Check the solution
• Practice and practice solving word problems

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