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

Step-by-step 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)

$58=8x+2$

$8x=58-2$

$8x=56$

$x=\frac{56}{8}$

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

Now substituting the value of equation 3 in equation 2.

$L=3x+1$

$L=(3\times 7)+1$

$L=21+1$

$L=22$

$L=22 inches$

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

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

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

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3 years ago