Given the perimeter of the rectangle = 304 ft.
The length of the rectangle given = (9a+10) ft
width of the rectangle given = (8a+6)ft
We know that the formula to find the perimeter of the rectangle is
2(length + width)
So by placing the values of length and width of the rectangle in the formula we will get,
[tex] 2((9a+10)+(8a+6)) [/tex]
= [tex] 2(9a+10+8a+6) [/tex]
We will add like terms now. Here like terms means a with a and constant term with constant term. So we will add 9a and 8a and also 10 and 6.
[tex] 2(9a+8a+10+6) [/tex]
= [tex] 2(17a+16) [/tex]
Now we will equate this perimeter with the perimeter given.
[tex] 2(17a+16) = 304 [/tex]
Now we have to move 2 to the other side by dividing it to both sides.
[tex] 2(17a+16) /2 = 304/2 [/tex]
[tex] 17a+16 = 304/2 [/tex]
[tex] 17a+16 = 152 [/tex]
We will move 16 now to the other side by subtracting it from both sides.
[tex] 17a+16-16 = 152 -16 [/tex]
[tex] 17a = 152-16 [/tex]
[tex] 17a = 136 [/tex]
Now to find a, we have to move 17 to the other side by dividing it to both sides.
[tex] 17a/17 = 136/17 [/tex]
[tex] a = 136/17 [/tex]
[tex] a = 8 [/tex]
So we have got the required answer.
The value of a = 8ft.
