Assuming you are referring to the area of a "trapezoid"; in which one calculates the Area, "A", as follows: ________________________ <span> A = 1/2* h(b1+b2) ;
in which: A = Area = 16 (given); h = height = 4 (given); b1 = length of one of the two bases = 3 (given); b2 = length of the other of the two bases = ? (what we want to solve for) ; ______________________________________________________ Using the formula: </span>A = 1/2 h(b1+b2) ; ________________________________ Let us plug in our known values: ___________________________ → 16 = (1/2) * 4*(3 + b2) ; → Solve for "b2". ________________________________ →Note: On the "right-hand side" on this equation: "(1/2)*(4) = 2 ." ________________________________ So, we can rewrite the equation as: ________________________________ → 16 = 2*(3 + b2) ; → Solve for "b2". ________________________________ We can divide EACH side of the equation by "2"; to cancel the "2" on the "right-hand side" of the equation: ________________________________ → 16 / 2 = [2*(3 + b2)] / 2 ; → to get: ___________________________ 8 = (3 + b2) ; _________________ → Rewrite as: 8 = 3 + b2; _______________________ Subtract "3" from EACH side of the equation; to isolate "b2" on one side of the equation; and to solve for "b2" : ______________________________ → 8 - 3 = 3 + b2 - 3 ; → to get: _____________________ b2 = 5; From the 2 (TWO) answer choices given, this value, "b2 = 5", corresponds with the following answer choice: ____________________ b2= [16-6]/2= 5 ; as this is the only answer choice that has: "b2 = 5". <span>_________________________________________
As far getting "</span>b2 = 5" from: "b2= [16-6]/2= 5"; (as mentioned in the answer choice), we need simply to approach the problem in a slightly different manner. Let us do so, as follows: <span>_____________________________________ Start from: </span>A = 1/2 h(b1+b2); and substitute our known (given) values):<span> ________________________ </span>→ 16 = (1/2) *4 (3 + b2) ; → Solve for "b2". _____________________________ Note that: (½)*4 = 2; so we can substitute "2" for: "(1/2) *4" ; and rewrite the equation as follows: _________________________ → 16 = 2 (3 + b2) ; ____________________ Note: The distributive property of multiplication: _________________________ a*(b+c) = ab + ac ; _________ As such: 2*(3 + b2) = (2*3 + 2*b2) = (6 + 2b2). _________________ So we can substitute: "(6 + 2b2)" in lieu of "[2*(3 + b2)]"; and can rewrite the equation: ______________________ → <span>16 = 6 + 2(b2) ; Now, we can subtract "6" from EACH side of the equation; to attempt to isolate "b2" on one side of the equation:</span> <span>________________________________________________ </span>→ 16 - 6 = 6 + 2(b2) - 6 ; → Since "6-6 = 0"; the "6 - 6" on the "right-hand side" of the equation cancel. → We now have: 16 - 6 = 2*b2 ; ___________ Now divide EACH SIDE of the equation by "2"; to isolate "b2" on one side of the equation; and to solve for "b2": ____________________ → (16 - 6) / 2 = (2*b2) / 2 ; → (16 - 6) / 2 = b2 ; → (10) / 2 = b2 = 5. ______________ NOTE: The other answer choice given: _____________ "<span>16= 1/2* 4(3+b2)= 6+2b2" is incorrect; since it does not solve for "b2".</span>