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ahrayia [7]
2 years ago
10

The area of a rectangular piece of metal is 1,984 square centimeters. The perimeter is 188 centimeters. What are the dimensions

of the piece?
Mathematics
1 answer:
gulaghasi [49]2 years ago
5 0

Answer:

There are 2 options:

  • x = 32 cm and y = 62 cm
  • x = 62 cm and y = 32 cm

Step-by-step explanation:

That's a rectangular piece, therefore let's consider the width to be x and the length to be y.

A = width * length

1) A = x * y = 1,984 cm^2

P = 2 * (width) + 2 * (length)

2) P = 2x + 2y = 188 cm

Isolate x or y in one of the equations.

xy = 1,984 cm^2

y = 1,984 cm^2 / x

Now plug it in the second equation.

2x + 2y = 188 cm

2x + 2 * (1,984 / x) = 188

Now we have only one variable. Now just solve it alegebraically.

2x + (3,968 / x) = 188

Multiply both sides by x in order to get rid of the fraction.

2x^{2} + 3968 = 188 x

Substract both sides by 188 x

2x^2 + 3968 - 188x = 0

Now divide by 2 to make the equation simpler.

x^2 - 94x + 1984 = 0

use the quadratic formula:

\frac{94 + \sqrt{(-94)^2 - 4(1)(1984)} }{2(1)} = 62\\\frac{94 - \sqrt{(-94)^2 - 4(1)(1984)} }{2(1)} = 32    

  x1 = \frac{-b + \sqrt{b^2 - 4ac} }{2a} \\x2 = \frac{-b - \sqrt{b^2 - 4ac} }{2a}

x is either 62 or 32.

let's find y:

y = 1,984 / x

y = 1,984 / 62 = 32

y = 1,984 / 32 = 62

There are 2 options:

  • x = 32 cm and y = 62 cm
  • x = 62 cm and y = 32 cm

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Step-by-step explanation:

\bf \: Given :

\sf \: Side  \:  of \:  the \:  square = 2.5 \: cm

\bf \: To \:  find:

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\bf \: Solution :

\rm \: First \:  w e \:  need \:  to \:  find  \: out  \: the  \: perimeter \:  o f \:  it.

So to find the Perimeter of the square, we'll use this formula :

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\bf \: Step\;2 : \rm Multiply :

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Hence, the perimeter would be 10 cm .

\rule{225pt}{2pt}

\sf \: Now,\; let's\; find  \: the  \: Area .

We know that the formula of Area to find the square is,

\boxed{ \sf \longrightarrow \: Area = (side) {}^{2} }

Note : The answer would always be in cm².

\bf Step\;  1  :\rm Put\;  the\; value \; of\;  side \; of \; the\; square :

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\bf \: Step\;2 : \rm Multiply :

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Hence, the area of the square would be 6.25 cm².

<em>We are done !</em>

\rule{225pt}{2pt}

I hope this helps!

Let me know if you have any questions.

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