Question

A retangle has a perimeter (p) of 58 inches. The length (L) is one more than 3 times the width (W)

Answer 1

The rectangle has a perimeter P of 58 inches.The length l is one more than 3 times the width w.write and solve a system of linear equations to find the length and width of the rectangle?

Answer:

Length(L)=22 inches

Width(W) = 7 inches

Explanation:

GIven:-

Perimeter (p)=58 inches,

Length(L)= one more than 3 times the width(W)

Let, W=x ---------------------------------(equation 1

`L=3x+1` -----------------------(equation 2)

Here x is unknown and to find the Width(W) we have to find the value of x.

Now,

Perimeter of rectangle(p) = 2 times length(L) + 2 times width(W)

`p=2L+2W`

`p=2(3x+1)+2x` ----------------(from equation 1)

`58=6x+2+2x` ----------------(given p=58 inches)

`58=8x+2`

`8x=58-2`

`8x=56`

`x=(56)/(8)`

`x=7` ----------------------(equation 3)

Now substituting the value of equation 3 in equation 2.

`L=3x+1`

`L=(3* 7)+1`

`L=21+1`

`L=22`

`L=22 inches`

as,
`W=x` -----------------------(from equation 1)

`W=7` inches -------------------(equation 3)

Therefore, Length(L) = 22 inches and Width(W) = 7 inches.