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,

$W=3+\frac{1}{4} L$

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

$5=3+\frac{1}{4} L$

subtract both sides 3

$5-3=3-3+\frac{1}{4} L$

$2=\frac{1}{4} L$

multiply both sides by 4

$4*2=4*\frac{1}{4} L$

$L=8$

so,

length of rectangle is 8 meter

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