Respuesta :
Answer:
y = 3x
2y + 2x = 85
x = 10 5/8 y = 31 5/8
Step-by-step explanation:
Let’s say that y = length and x = width. We know that the length is 3 times the width (y = 3x) and the perimeter of the rectangle is 85 (2y + 2x = 85). To solve the system of equations, substitute y = 3x into the other equation. This results in the equation 2(3x) + 2x = 85. We now simplify the equation. 6x + 2x = 85 8x = 85 x = 10 5/8.
Now that we know x, we can substitute it into either equation to solve for y. y = 3(10 5/8) y = 31 5/8
The system of equation which represent the given situation is 85 = 8x.
And the length and width of the rectangle is 36.86 and 10.62unit respectively.
What is perimeter?
Perimeter is the distance around the edge of a shape.
Formula for the perimeter of a rectangle
[tex]P = 2(l+w)[/tex]
where,
P is the perimeter of the rectangle
l is the length of the rectangle
w is the width of the rectangle.
According to the given question here:
We have,
The perimeter of the rectangle is 85 unit.
Let the width of the rectangle be x unit.
Then, the length of the rectangle be 3x.
Therefore, the equation which represent the situation is given by
85 = 2(x + 3x)
⇒85 = 2(4x)
⇒ 85 =8x
⇒ x = 85/8 = 10.62unit
⇒ 3x = 10.62 × 3 = 31.86 unit.
Hence, the length of the given rectangle is 31.86 unit and width is 10.62 unit .
Learn more about the perimeter of the rectangle here:
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