Question

The perimeter of the rectangle with sides `8a+6` and `9a + 10` is 304 ft. What are the values of its sides?

Answer 1

`82" and "70" feet"`

Explanation:

`"the perimeter of a rectangle is"`

`•color(white)(x)"perimeter "=2l+2b`

`"where "l" is the length of one side and " b" the"`
`"length of the other side"`

`"let "l=9a+10" and "b=8a+6`

`rArr2l+2b=2(9a+10)+2(8a+6)`

`color(white)(xxxxxxx)=18a+20+16a+12`

`color(white)(xxxxxxx)=34a+32`

`"now perimeter "=304`

`rArr34a+32=304`

`"subtract 32 from both sides"`

`34acancel(+32)cancel(-32)=304-32`

`rArr34a=272`

`"divide both sides by 34"`

`(cancel(34) a)/cancel(34)=272/34`

`rArra=8`

`"one side "=(8xx8)+6=64+6=70" feet"`

`"other side "=(9xx8)+10=72+10=82" feet"`

`color(blue)"As a check"`

`"perimeter "=(2xx70)+(2xx82)=140+164=304" feet"`