Question

A rectangle has length 1/2 x + 5 and width 1/4 x + 4 If the perimeter of the rectangle is 42 meters, write and solve an equation to find the length and the width of the rectangle?

Answer 1

Length is 13

and width is 8

Explanation:

we have to use the following formula here,

perimeter of rectangle=2(length+width)

So, here we get

`2((1)/(2) x+5+ (1)/(4) x+4)=42\\ or, 2((1)/(2) x +(1)/(4) x+9)=42\\or, x+(x)/(2) +18=42\\or, (2x+x)/(2)=42-18 \\or, (3x)/(2) =24\\or, 3x=48\\or, x=(48)/(3) =16`

So,

length=
`(1)/(2) (16)+5=8+5=13`

width=
`(1)/(4) (16)+4=4+4=8`