Question

Define a variable write an equation and solve the problem. the width of a rectangle is 3 meters more than one-fourth its length. the perimeter is 10 meters more than twice its length. find the length and width

Answer 1

Let's assume

length of rectangle is L

width of rectangle is W

the width of a rectangle is 3 meters more than one-fourth its length

so,

`W=3+(1)/(4) L`

the perimeter is 10 meters more than twice its length

we know that

perimeter =2(L+W)

so, we get

`2(L+W)=10+2L`

now, we can simplify it

`2L+2W=10+2L`

subtract both sides by 2L

`2L+2W-2L=10+2L-2L`

`2W=10`

`W=5`

now, we can find L

`5=3+(1)/(4) L`

subtract both sides 3

`5-3=3-3+(1)/(4) L`

`2=(1)/(4) L`

multiply both sides by 4

`4*2=4*(1)/(4) L`

`L=8`

so,

length of rectangle is 8 meter

width of rectangle is 5 meter ............Answer