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navik [9.2K]
3 years ago
11

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

Mathematics
1 answer:
worty [1.4K]3 years ago
7 0

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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