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This Is Treasure Hunt (mr Shape) - Education - Nairaland

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This Is Treasure Hunt (mr Shape) by Mrshape: 11:49am On May 04
Find the square , if you can find it, them find its area

Re: This Is Treasure Hunt (mr Shape) by Mrshape: 12:47pm On May 04
Anyone?
Re: This Is Treasure Hunt (mr Shape) by femi4: 1:36pm On May 04
(6-X)²+4² = 4² +(4+X)²
36-12X+ X²= 16 + 8X + X²
20x = 20
X = 1
Area of the square = 1² = 1unit²
Re: This Is Treasure Hunt (mr Shape) by Martinez39: 5:20pm On May 04
grin cheesy

A = (24 - 8√5) ÷ 5 ≈ 1.22229124 unit².

Cc. Mrshape
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 6:45pm On May 04
Show your workings
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 7:45am On May 05
femi4:
(6-X)²+4² = 4² +(4+X)²
36-12X+ X²= 16 + 8X + X²
20x = 20
X = 1
Area of the square = 1² = 1unit²
Try again sir







Re: This Is Treasure Hunt (mr Shape) by Mrshape: 7:45am On May 05
Martinez39:
grin cheesy

A = (24 - 8√5) ÷ 5 ≈ 1.22229124 unit².

Cc. Mrshape
Try again sir
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 7:54am On May 05
Should I drop workings?
Re: This Is Treasure Hunt (mr Shape) by Darivie04(m): 8:27am On May 05
Mrshape:
Should I drop workings?
Yes
Re: This Is Treasure Hunt (mr Shape) by femi4: 8:46am On May 05
[quote author=Mrshape post=78115557][/quote]This should do it

A rectangle is formed at the centre by merging the two squares.

So if x is the length of the square
L of the rectangle = 2x
b of the rectangle = length of the square = x
Diagonal = x√5

Now
4² + 4² = (4+ x√5)²

32 = (4+x√5)²
4+x√5 = 4√2
x = (4√2 - 4)/√5
Area of the square = x² = (4√2 - 4 )²/5 = 0.5490unit²

Re: This Is Treasure Hunt (mr Shape) by RolD: 9:15am On May 05
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 10:13am On May 05
femi4:
This should do it

A rectangle is formed at the centre by merging the two squares.

So if x is the length of the square
L of the rectangle = 2x
b of the rectangle = length of the square = x
Diagonal = x√5

Now
4² + 4² = (4+ x√5)²

32 = (4+x√5)²
4+x√5 = 4√2
x = (4√2 - 4)/√5
Area of the square = x² = (4√2 - 4 )²/5 = 0.5490unit²
No sir, I will post solution soon
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 10:27am On May 05
Solution.

Re: This Is Treasure Hunt (mr Shape) by Mrshape: 10:32am On May 05
If you have any objection or questions regarding my solution feel free to ask.
Re: This Is Treasure Hunt (mr Shape) by Darivie04(m): 11:34am On May 05
Mrshape:
Solution.
Can you explain some of the intuition and reasoning behind the solution in words?
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 11:39am On May 05
Darivie04:

Can you explain some of the intuition and reasoning behind the solution in words?

Ok sir
I will
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 11:56am On May 05
Darivie04:

Can you explain some of the intuition and reasoning behind the solution in words?
Divide the Shape into two parts by drawing a symmetrical line as shown in the diagram.
Since the square is between two circles it is obvious the line will divide the square into a rectangle of top lenght 1/2(lenght of square and the other side of the rectangle will be also equal to the square lenght because it was not divided
Next form a right angled triangle by projecting a vertical line from the vartice of the rectangle to interseect at right angle with an horizontal line draw from the center of the circle.
Note the vertical line will (radius (2)-lenght of square)
The horizontal line will be (radius(2) -1/2 lenght of the square)
And the hypotenuse is =radius (2)
Since the vertical and horizontal line must intersect at right angle
(2-0.5x)^2+(2-x)^2=2^2.
The rest are algebra......
Re: This Is Treasure Hunt (mr Shape) by Mrshape: 12:00pm On May 05
femi4:
This should do it

A rectangle is formed at the centre by merging the two squares.

So if x is the length of the square
L of the rectangle = 2x
b of the rectangle = length of the square = x
Diagonal = x√5


Now
4² + 4² = (4+ x√5)²

32 = (4+x√5)²
4+x√5 = 4√2
x = (4√2 - 4)/√5
Area of the square = x² = (4√2 - 4 )²/5 = 0.5490unit²
From your diagram the diagonal of the right angle must not always pass through both centers of the circles the vartices are touching,
That's were you got it wrong sir.
Re: This Is Treasure Hunt (mr Shape) by femi4: 1:23pm On May 05
Mrshape:
If you have any objection or questions regarding my solution feel free to ask.
No objection, I tried that route and got some negative values.

1 Like

Re: This Is Treasure Hunt (mr Shape) by Mrshape: 1:37pm On May 05
femi4:
No objection, I tried that route and got some negative values.
You are welcome sir.

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