Answer:
The answer to your question is l = 12 and w = 7/2 or 3.5
Step-by-step explanation:
Data
length = l
width = w
Area = 42 yd²
Process
1) Write equations that help to solve this problem
Area = length x width = l x w
Length = 2width + 5 or l = 2w + 5
2) Substitution
42 = lw Equation l
l = 2w + 5 Equation ll
42 = (2w + 5)w Substitute equation ll in l
3.- Expand
42 = 2w² + 5w
2w² + 5w - 42 = 0
Solve the equation by factoring
-Multiply 2 by 42
2 x 42 = 84
-Find the prime factors of 84
84 = 2² 3 7
-Find two numbers that added gives +5 using the prime factors
These numbers are +12 and -7
-Substitute the values in the equation
2w² -7w + 12w - 42
-Factor by grouping
w(2w - 7) + 6(2w - 7)
(2w - 7)(w + 6)
-Find w
2w₁ - 7 = 0 w₂ + 6 = 0
w₁ = 7/2 w₂ = -6 This value is discarted because
there are no negative values
-Find l
l = 2(7/2) + 5
l = 7 + 5
l = 12
