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USPshnik [31]
3 years ago
5

The perimeter of a rectangle is 60 cm. The ratio of length to width is 3:2 . Find the length and width of the rectangle.

Mathematics
1 answer:
Alona [7]3 years ago
8 0

x = length

y = width

---

2x + 2y = 60

x/y = 3/2

2x = 3y

---

put the system of linear equations into standard form

---

2x + 2y = 60

2x - 3y = 0

---

solution:

length = 18 cm

width = 12 cm

Hope this helps!

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Answer:

y =  -  \frac{ 1 }{10} {x}^{2}   +  \frac{5}{2}

Step-by-step explanation:

We want to prove algebraically that:

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We use the relations

{r}^{2}  =  {x}^{2}  +  {y}^{2}

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Before we substitute, let us rewrite the equation to get:

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Or

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Expand :

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We now substitute to get:

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This means that:

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Square:

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Expand:

{x}^{2}  +  {y}^{2} =25 - 10y +  {y}^{2}

{x}^{2}  =25 - 10y

{x}^{2}  - 25 =  - 10y

y =  -  \frac{ {x}^{2} }{10}  +  \frac{5}{2}

This is a parabola (0,2.5) and turns upside down.

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