how do i find the length of(read on)?

Question

a diagnal in a square that has a perimeter of 48 inches. This is 10th grade geometry and i suck at it any help would be greatly aprreciated please by tonight i nned this for test tommorrow THANK YOU

then what is the simplified radical form of √288?

Answer 1

Let x equal the length of one of the sides.

So you now know that 4x = 48 in, so x = 12 in.
The diagonal (or hypontenuse) is the positive square root of the sum of the sides since it is square.
Let d equal the length of the diagonal.
d^2 = x^2 + x^2
d^2 = 12^2 + 12^2
d^2 = 144 + 144
d^2 = 288
d = 16.971 in (approx.)

Answer 2

Ok, basically all you have to do is split the square into two triangles, by putting a diagonal line from the upper left corner of the square to the bottom right.

Then you have to figure out the measure of each side of the square. Since you have a 48 inch perimeter, then you just do 48/4. Thats 12 inches to each side

So the two "legs" of your triangle are 12 and 12

This is where the pythagorean theorem comes in.

A² + B² = C²

(Leg 1)² + (Leg 2)² = (Diagonal of Triangle/Hypoteneuse)²

So easy as this...
(12)² + (12)² = C²

144+144 = C²

288 = C²

In order to get C, which is what your going for, your going to have to square root BOTH sides.

So C = √288
C ≈ 16.97

Hope this helps, I know this is sophomore geometry, so you may have known some of this already. Good Luck on your test!!!

Answer 3

No problem.

1) The perimeter of a square, divided by 4 give you the length of
each side. 48" / 4 = 12"

2) In a square, each corner is a right (90 degree) angle.
3) A diagonal line from corner to the opposite corner will divide it into two right triangles.
4) The diagonal is the hypotenuse of each right triangle.
5) Use the Pythagorean theorem (A2 + B2 = C2)
6) In this case, A=B. (each is the side to the square)
7) To solve for C:
a) Square A and Square B, add the two together
b) The square root of the result is 'C', the diagonal.

So...

A2 = 12*12 = 144
B2 = 12*12 = 144
A2 + B2 = 288
C = the square root of 288, or 16.97056275
Check my math. It's been a while since I did geometry.

Good luck!

Answer 4

If the square has a perimenter of 48 inches, each side must be 48/4 or 12 inches.

So we have a right triangle with the two legs of 12 inches each. We need to find the hypotenuse.

a^2 + b^2 = c^2
12^2 + 12^2 = c^2
c^2 = 288
c (diagonal) = 288^0.5 or (144)2^0.5

Answer 5

I misread, but this is how you would solve if the diagonal was 48. It is pretty much the same concept.

A square has four equal sides. Since the diagonal cuts the square from one corner to the opposite, you can think of it as the hypotenuse of two triangles. The square has right angles, so the diagonal makes right triangles. Use the pythagoream theorem, a^2+b^2=c^2. You can see that a and b are equal because they are sides of the square. So, x^2+x^2=2x^2.

2x^2=48^2
x^2=1152

x=24(sqrt2)

Answer 6

im sorry i cant tell you the answer but if you go to MATH.COM they have all the answers for all types of questions and it is a really easy site to use
hope this helps