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how long is the diagonal of a square that has an area of 1000 square centimeters? express your answer as a decimal to the nearest tenth. I came up with .5cm is that correct?

2007-12-09 04:52:54 · 9 answers · asked by sheba40 1 in Science & Mathematics Mathematics

9 answers

The area of a square is L² where L is the length of one side.

L² = 1000 cm²
L = sqrt ( 1000 ) cm
L = 31.63 cm

The diagonal is the hypotenuse of a right trangle where the other two sides have length L. The Pythagorean theorem tells us that

H² = L² + L²

We already know that L² = 1000 so

H² = 2000
H = sqrt ( 2000 ) cm
H = 44.72 cm

2007-12-09 04:59:56 · answer #1 · answered by jgoulden 7 · 0 0

The diagonal of a square is always the length of the side multiplied by the square root of 2. This means that the lengths of the sides of the squares are also proportional, the larger square having a side 4 times that of the smaller. The area is thus 16 times larger. Ex. Large square has diagonal 4*square root 2. Small square has diagonal 1*square root 2. Side length of the large square is 4 and the side length of the small square is 1. 4^2=16. 1^2=1. 16/1=16

2016-05-22 08:02:25 · answer #2 · answered by ? 3 · 0 0

You first take the square root of 1000, that's the length of each side. Then you square that twice and take the square root of the sum. But since the square of the square root of 1000 is 1000, you can just take the square root of 1000+1000, or the square root of 2000, that's the answer, about 44.7 cm

2007-12-09 05:00:48 · answer #3 · answered by Mikey 2 · 0 0

Given: Area of the Square = (Side)^2 = 1000 sq. cms.

Hence Side = √(1000).

Now by Pythagoras Theorem:

Hypotenuse of the square = √2*Side

≈ √(2000) ≈ 44.721 cms.

2007-12-09 05:07:48 · answer #4 · answered by quidwai 4 · 0 0

If the area is 1000, then each side must be 31.62... Using pythagorean therom, a2 + b2 = c2, you get 1000 + 1000 = 2000. So the diagonal must be the square root of 2000 which is 44.72

2007-12-09 05:00:16 · answer #5 · answered by krock19usa2008 1 · 0 0

If the area = 1000, then the side length is sqrt(1000) = 31.63

Using the pythagorean theorem we can say that a diagonal (d) is:

d^2 = s^2 + s^2 = 2s^2 = 2*1000 = 2000
d = sqrt(2000) = 44.7cm

Hope this helps! :)

2007-12-09 04:58:26 · answer #6 · answered by disposable_hero_too 6 · 0 0

Area of square = 1000
Therefore each side sqrt1000=31.62

By Pythagoras Theorem
31.62^2+31.62^2=1999.6488

sqrt1999.6488=44.7 This is your answer

2007-12-09 05:01:44 · answer #7 · answered by C63AMG 5 · 0 0

No.
Ld = √1000*√2 = 44.7 cm

2007-12-09 04:58:44 · answer #8 · answered by Steve 7 · 0 0

The sides have to be 31.623 cm
Then use Pythegorian(?) Theorm. 31.623^2+31.623^2=x^2
Solve for x
I got 44.722 cm

2007-12-09 04:57:13 · answer #9 · answered by ひいらぎ 5 · 0 0

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