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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) ;

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Using the formula:

A = 1/2 h(b1+b2) ;

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Let us plug in our known values:

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→ 16 = (1/2) * 4*(3 + b2) ; → Solve for “b2”.

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→Note: On the “right-hand side” on this equation: “(1/2)*(4) = 2 .”

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So, we can rewrite the equation as:

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→ 16 = 2*(3 + b2) ; → Solve for “b2”.

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We can divide EACH side of the equation by “2”; to cancel the “2” on the “right-hand side” of the equation:

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→ 16 / 2 = [2*(3 + b2)] / 2 ; → to get:

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8 = (3 + b2) ;

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→ Rewrite as: 8 = 3 + b2;

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Subtract “3” from EACH side of the equation; to isolate “b2” on one side of the equation; and to solve for “b2” :

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→ 8 – 3 = 3 + b2 – 3 ; → to get:

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b2 = 5; From the 2 (TWO) answer choices given, this value,

“b2 = 5”, corresponds with the following answer choice:

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b2= [16-6]/2= 5 ; as this is the only answer choice that has: “b2 = 5”.

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As far getting “

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:

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Start from: A = 1/2 h(b1+b2); and substitute our known (given) values):

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→ 16 = (1/2) *4 (3 + b2) ; → Solve for “b2”.

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Note that: (½)*4 = 2; so we can substitute “2” for: “(1/2) *4” ;

and rewrite the equation as follows:

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→ 16 = 2 (3 + b2) ;

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Note: The distributive property of multiplication:

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a*(b+c) = ab + ac ;

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As such: 2*(3 + b2) = (2*3 + 2*b2) = (6 + 2b2).

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So we can substitute: “(6 + 2b2)” in lieu of “[2*(3 + b2)]”; and can rewrite the equation:

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→ 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:

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→ 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 ;

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Now divide EACH SIDE of the equation by “2”; to isolate “b2” on one side of the equation; and to solve for “b2”:

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→ (16 – 6) / 2 = (2*b2) / 2 ;

→ (16 – 6) / 2 = b2 ;

→ (10) / 2 = b2 = 5.

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NOTE: The other answer choice given:

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“16= 1/2* 4(3+b2)= 6+2b2″ is incorrect; since it does not solve for “b2”.