Question

The width of a rectangle is 4 inches greater than half the length. The perimeter is 56 inches. What is the length and the width of the rectangle

Answer 1

Answer:

Length of the rectangle = 16 inches

Width of the rectangle = 12 inches

Step-by-step explanation:

Let the length of the rectangle be represented by x.

Then width can be expressed as $\[\frac{x}{2}+4\]$

Perimeter of a rectangle is the sum of four sides of the rectangle.

This can be expressed as 2*(length + breadth)

= $\[2* (x + \frac{x}{2}+4)\]$

= $\[2* (\frac{3x}{2}+4)\]$

= $\[3x + 8\]$

But perimeter is given as 56.

So, $\[3x + 8 = 56\]$

=> $\[3x = 48\]$

=> $\[x = 16\]$

Hence length of the rectangle = 16 inches

Width of the rectangle = $\[\frac{16}{2}+4\]$ = 12 inches

Answer 2

Answer:

length = 16 inches and width = 12 inches

Step-by-step explanation:

Let l be the length and w be the width of the rectangle.

It is given that width is 4 inches greater than half of the length:

$w=\frac{l}{2}+4$ ------1

Perimeter of the rectangle is given by $2\times(l+w)$

$2\times(l+w)=56$

$l+w=28$  ----------------2

Substituting w from equation 1 in equation 2, we get:

$l+(4+\frac{l}{2})=28$

$\frac{3l}{2}=24$

∴ l = 16 inches

Putting l=16 in equation 1, we get w=12.

Hence w= 12 inches.