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

Answer:

Length is 13

and width is   8

Step-by-step explanation:

we have to use the following formula here,

perimeter of rectangle=2(length+width)

So, here we get

$2(\frac{1}{2} x+5+ \frac{1}{4} x+4)=42\\ or, 2(\frac{1}{2} x +\frac{1}{4} x+9)=42\\or, x+\frac{x}{2} +18=42\\or, \frac{2x+x}{2}=42-18 \\or, \frac{3x}{2} =24\\or, 3x=48\\or, x=\frac{48}{3} =16$

So,

length=$\frac{1}{2} (16)+5=8+5=13$

width=$\frac{1}{4} (16)+4=4+4=8$