Respuesta :
The width is 6 inches and the length is 26 inches.
Explanation:
L=4w+2, since the length is 2 more than 4 times the width.
The perimeter is given by P=2L+2w; using our equation for L, we have
P=2(4w+2)+2w.
Using the distributive property, we have
P=2*4w+2*2+2w
P=8w+4+2w.
Combining like terms, we have P=10w+4.
We know the perimeter is 64, so we have
64=10w+4.
Subtract 4 from both sides:
64-4=10w+4-4
60=10w.
Divide both sides by 10:
60/10 = 10w/10
6=w.
Substitute this into the equation for length: L=4*6+2=24+2=26
Explanation:
L=4w+2, since the length is 2 more than 4 times the width.
The perimeter is given by P=2L+2w; using our equation for L, we have
P=2(4w+2)+2w.
Using the distributive property, we have
P=2*4w+2*2+2w
P=8w+4+2w.
Combining like terms, we have P=10w+4.
We know the perimeter is 64, so we have
64=10w+4.
Subtract 4 from both sides:
64-4=10w+4-4
60=10w.
Divide both sides by 10:
60/10 = 10w/10
6=w.
Substitute this into the equation for length: L=4*6+2=24+2=26
Answer:
Length of the rectangle = 26 inch
Width of the rectangle = 6 inch
Step-by-step explanation:
Let the width of the rectangle be ‘ w ‘
Length of the rectangle
l = 4 w + 2 inches
Perimeter of a rectangle = 2 time of sum of its length and width
= 2 ( w + l) ------------------------equation (1)
Substituting the value of l in equation 1, we get –
2 (w + (4 w + 2)) = 64 inches
2w + 8w + 4inches = 64 inches
10w = 64 inches - 4inches
10 w = 60 inches
w = 6 inches
Length of the rectangle = 4w + 2inch
= 4 x 6 inches + 2 inch
= 24 inch + 2 inch
= 26 inch
Thus,
Length of the rectangle = 26 inch
Width of the rectangle = 6 inch
