Question

The length of a rectangle is 3 centimeters more than 3 times the width. If the perimeter of the rectangle is 46 centimeters, what are the dimensions of the rectangle?

Answer 1

length = 18cm , width = 5cm

Explanation:

Begin by letting width = x then length = 3x + 3

Now perimeter ( P ) `=(2xx" length" )+ (2xx" width")`

`rArrP=color(red)(2)(3x+3)+color(red)(2)(x)`

distribute and collect 'like terms'

`rArrP=6x+6+2x=8x+6`

However, P is also equal to 46, so we can equate the 2 expressions for P.

`rArr8x+6=46`

subtract 6 from both sides of the equation.

`8x+cancel(6)-cancel(6)=46-6rArr8x=40`

divide both sides by 8 to solve for x.

`rArr(cancel(8)^1 x)/cancel(8)^1=cancel(40)^5/cancel(8)^1rArrx=5`

Thus width = x = 5cm and length = 3x+3 = 15 + 3 = 18cm

check: `(2xx5)+(2xx18)=10+36=46 " hence correct."`