The width of a rectangular window frame is 12 inches less than its length. if you add 30 inches to both the length and the width, you double the perimeter. find the length and the width of the original rectangle?

Let's assume

length of rectangle is x

width of rectangle is y

we are given

The width of a rectangular window frame is 12 inches less than its length

so, we get

now, we are given

if you add 30 inches to both the length and the width, you double the perimeter

perimeter of rectangle =2*length+2*width

perimeter of rectangle =

After adding 30 inches,

perimeter will become =

and it is double of original

so, we get

now, we can simplify it

so, we will get system of equations as

first equation:

Second equation:

now, we can solve it by using substitution

we can plug first equation into second equation

now, we can find y

so, dimensions of rectangle are

length is 36 inches

width is 24 inches..............Answer

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: