Question

If the perimeter is 284, what is the value of a? Please show work xx

Answer 1

Answer:  The required value of a is 8.

Step-by-step explanation:  Given that the perimeter of the trapezoid shown is 284 units.

We are to find the value of a.

From the figure, we note that

the lengths of the sides of the trapezoid are 12a, 6a+8, 10a-4 and 6a+8.

We know that

the perimeter of any polygon is equal to the sum of the lengths of the sides of the polygon.

Therefore, for the given trapezoid, we must have

$12a+6a+8+10a-4+6a+8=284\\\\\Rightarrow 34a+12=284\\\\\Rightarrow 34a=284-12\\\\\Rightarrow 34a=272\\\\\Rightarrow a=\dfrac{272}{34}\\\\\Rightarrow a=8.$

Thus, the required value of a is 8.

Answer 2

Answer:

8

Step-by-step explanation:

Perimeter is 284 means the sum of the side measurements is 284.

That is, we have to solve:

$(6a+8)+(12a)+(10a-4)+(6a+8)=284$

Combine like terms:

$(6a+12a+10a+6a)+(8+0+-4+8)=284$

Simplify:

$34a+12=284$

Subtract 12 on both sides:

$34a=284-12$

Simplify:

$34a=272$

Divide both sides by 34:

$a=\frac{272}{34}$

Simplify:

$a=8$