Respuesta :
Answer: The length is 62 inches and the width is 13 inches
Step-by-step explanation: The perimeter of the rectangular portrait has been given as 150 inches. We also know that the perimeter of a rectangle is given as
Perimeter= 2(L + W)
However we don't have the measurements for the length and width. What we do have are descriptions of both. The length is given as W, while the length is ten more than four times the width. That is, the length equals
10 + 4W
Therefore we have the length and the width as
L = 4W + 10 and
W = W
If the perimeter is 150, and
Perimeter = 2(L + W) then,
150 = 2(4W + 10 + W)
150 = 2(5W + 10)
150 = 10W + 20
Subtract 20 from both sides of the equation
130 = 10W
Divide both sides of the equation by 10
13 = W
With that in mind we can now calculate the length as
L = 4W + 10
Substitute for the value of W
L = 4(13) + 10
L = 52 + 10
L = 62
Therefore, the length is 62 inches and the width is 13 inches
Answer:
Length = 62 inches, Width = 13 inches
Step-by-step explanation:
Let L represent the length of the frame, W, the width and P, the perimeter
Perimeter of a rectangle, P = 2 (L + W) .....eq 1
Also, P = 150 inches
and
L = 10 + 4W .....eq 2
Slotting in the respective values of P and L in eq 1
150 = 2 {(10 + 4W) + W}
Expanding the bracket
150 + 2 (10 + 5W)
150 = 20 + 10W
Subtracting 20 from both sides of the equation
150 - 20 = 20 - 20 + 10W
130 = 10W
Dividing both sides by the coefficient of W which is 10
13 = W
Therefore, W = 13 inches
Slotting in the value of W in eq 2
L = 10 + 4 (13)
L = 10 + 52
L = 62 inches
Lets ensure that the values of L and W are correct
P = 2 (L + W)
150 = 2 (13 + 62)
150 = 2(75)
150 = 150
Hence, L = 62 inches, W = 13 inches
