The perimeter of a rectangle = 80m. The length is decreased by 7m and the width increased by 7m

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Жыл бұрын

How to find the perimeter of a figure - algebra word problem.
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Пікірлер: 17

@CzJanusz Жыл бұрын

I used two variables: I think there is a simpler approach using two variables: l for length and w for width. According to the requirements of this exercise perimeter can be determined as follows: 2l + 2w = 80 Now length decreased by 7 should be equal to the width increased by 7, sin this is a square. Therefore step by step: l - 7 = w + 7 +7 +7 l = w + 14 Let us substitute l in the first equation: 2 (w + 14) + 2w = 80 /2 2w + 28 + 2w = 80 4w + 28 = 80 /4 w + 7 = 20 -7 -7 w = 20 - 7 = 13 From above l = w + 14 l = 13 + 14 = 27 Check 2 * 27 + 2 * 13 = 54 + 26 = 80

@dianemier5335 Жыл бұрын

I used the perimeter would stay 80m, so each side of the resulting square would be 20m. Length minus 7 = 20 L= 27m Width plus 7 = 20. W = 13.

@Pandemonis Жыл бұрын

Elegant, this one is even quicker.

@dryster123 Жыл бұрын

I did not see why it was a problem, perimeter stayed the same at 80m and it was a square, so each side was 80/4 = 20m

@tomtke7351 Жыл бұрын

There are two unknowns: L -- length W -- width two unknowns requires two equations. eq.1: perimeter around rectangle; 2 lengths and 2 widths summed: eq.1: 2L + 2W = 80m eq.2: a square means length = width. or eq.2: L - 7 = W + 7 eq.1: 2L + 2W = 80m eq.2: L - 7 = W + 7 eq.2 vrevised L - 7 = W + 7 L - W = 14 2L - 2W = 28 eq.2.2 eq.1: 2L + 2W = 80m eq.2.2 2L - 2W = 28 Added together ==> 4L = 108m eq.3 L = 27 ans.1 eq.2: L - 7 = W + 7. solve with L = 27 27 - 7 = W + 7 27 - 14 = W W = 13 ans.2 VERIFY: L = 27m W = 13m eq.1: 2L + 2W = 80m eq.2: L - 7 = W + 7 eq.1: 2L + 2W = 80m 2(27) + 2(13) =? 80 54 + 26 == 80 ✔️✔️✔️ eq.2: L - 7 = W + 7 27 - 7 =? 13 + 7 20 == 20 ✔️✔️✔️

@michaelholcombe3336 Жыл бұрын

did it in my head in 30 sec

@kevingeier3385 Жыл бұрын

The rectangle is 27 by 13. Since the perimeter has not changed. A square has 4 equal side. 80 divided by 4.

@quantisedspace7047 Жыл бұрын

The perimeter gets it's width and length increased and reduced in equal amounts, so the perimeters of the rect and square must be the same. The sides of the square are thus 20m. The sides of the original rect are thus 27 and 13

@monroeclewis1973 Жыл бұрын

The 80m perimeter remains the same because the 7m gain to each of the long sides of the rectangle is offset by the 7m loss to each of the short sides. The perimeter of any square is 4 times the side. Therefore, the side must be 80/4 = 20m. Working backwards, the dimensions of the original rectangle must be 20 + 7= 27m, and 20 - 7 = 13m.Just logic. No algebra.

@calvinmasters6159 7 ай бұрын

Fun way to round off an evening of bourbon. Keep 'em coming.

@gd-pythonica Жыл бұрын

The width is 13 meters and length is 27 meters. 1. Set up an equation for the perimeter that will help us solve for the sides: 2l+2w=80. 2. Set up another equation for the second clue. Since a square's sides are equal, L-7=W+7. 3. You now have a system of equations. You can solve for both variables and you will find that the width is 13m and the length is 17m.

@bobcornwell403 Жыл бұрын

The rectangle is 27 meters long and 13 meters wide.

@danieldennis9831 Жыл бұрын

I got 27 x 13

@aliso-pv7ll Жыл бұрын

Dear Mr. KZfaq Mathman, tell algebra to grow up! Solve your own problems!

@vjeraknezevic5889 Жыл бұрын

This is not right solution......process is not good

@Pandemonis Жыл бұрын

Video two long, didn't watch, its faster to make the maths by head than to type it : Given a for width and b for length, 2a + 2b = 80 Given the square information, a - 7 = b + 7, so a = b +14 so 2 (b+14) + 2b = 80 so 4b = 80 - 28 = 52, Solution for b = 13 a = 13 + 7 + 7 = 27

@vjeraknezevic5889 Жыл бұрын

Are you a teacher, what are you doing, repeating the same wrong things many time.....