Perfomance Task #4 Problem Solving involving Polynomial Equation
The length of a rectangular lot is 2 meters more than its width, find its dimensions if the area of the lot is 120 square meters?
The length of a rectangular lot is 2 meters more than its width, find its dimensions if the area of the lot is 120 square meters?
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Answer:
FORMULA:
Area = length × width
GIVEN:
Let x be the width
•length --- x+2
•Area --- 120 meters
COMPUTATION:
A = l×w
•Substitute values and simplify:
120 = (x+2)(x) ---- Eq. 1
120 = x²+2x
•Set equation to zero:
x²+2x-120 = 0
•Factor:
(x-10)(x+12) = 0
•From the step we just did we already have the dimensions.
•Find the value of x:
x_1
x-10=0
x = 10
x_2
x+12=0
x = -12
•Plug in both values of x to Eq. 1:
If x = 10, then:
120 = (x+2)(x)
120 = (10+2)(10)
120 = (12)(10)
120 = 120
TRUE
If x = -12, then:
120 = (x+2)(x)
120 = (-12+2)(-12)
120 = (-10)(-12)
120 = 120
TRUE
DIMENSIONS
length --- 12 meters
width --- 10 meters
The rectangular lot is 12 meters x 10 meters
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