The width of a card is 3 centimeters shorter than the length. The area is 46.75 square centimeters. What is the perimeter?

Answer 1

Perimeter is #40# #cm.#

Let the length be #x# #cm.# Ten width is #(x-3)# #cm# and as area of card is #46.75# #cm^2#.
Hence #x(x-3)=46.75# or #x^2-3x=46.75# and multiplying by #4#, we get
#4x^2-12x=187#
or #4x^2-12x-187=0#
i.e. #4x^2-34x+22x-187=0#
i.e. #2x(2x-17)+11(2x-17)=0#
i.e #(2x+11)(2x-17)=0#
As #2x+11# cannot be zero, we have #2x-17=0# i.e. #x=17/2=8.5#
Hence length is #8.5# and width is #11.5-3=8.5#
and perimeter is #2xx(11.5+8.5)=2xx20=40# #cm.#
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Answer 2

To find the perimeter of the card, we need to first find the length and width. Let's denote the length of the card as L centimeters and the width as W centimeters.

Given that the width is 3 centimeters shorter than the length, we can express the width as W = L - 3.

We also know that the area of a rectangle is given by the formula: Area = length × width. Therefore, we can write the equation for the area of the card as:

L × (L - 3) = 46.75

Expanding and rearranging the equation, we get a quadratic equation:

L^2 - 3L - 46.75 = 0

We can solve this quadratic equation to find the length of the card. Once we find the length, we can substitute it back into the expression for the width to find the width of the card.

After finding the length and width, the perimeter of a rectangle is given by the formula: Perimeter = 2(length + width).

We can substitute the values of length and width into this formula to find the perimeter of the card.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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