A piece of wire 12 in. long is bent to form a right triangle in which the shortest side is 2 in. Find the leng

Question

Find the lengths of the other two sides.

Answer 1

You're making a right traingle with sides 2, x, and y,
where 2 + x + y = 12, or x + y = 10.

Let y = 10 - x.

This gives you sides 2, x, and 10 - x, which do add to 12. Use the Pythagorean theorem to solve for x.

2² + x² = (10 - x)²
4 + x² = 100 - 20x + x²
20x = 96
x = 96 / 20 = 24 / 5 = 4.8

The lengths are 2, 4.8, and 5.2 inches.

Answer 2

Call the second leg of the triangle x. So then you have:

2 + x + h = 12
x + h = 10
h = 10 - x

So the three sides are 2, x, and 10 - x, in order of length. Then use the Pythagorean Theorem:

2 ^ 2 + x ^ 2 = (x - 10) ^ 2
4 + x ^ 2 = x ^ 2 - 20x + 100
20x = 96
x = 96/20
x = 24/5

So that means that the other two sides are 24/5 and 10 - 24/5, or 26/5.

Answer 3

Everyone else has different answers, so I'll try this one. You say the short side is 2, and the perimeter is 12. I'll call the long side x, so the hypoteneuse is sqrt(x^2 + 4).

Now we add the three sides together to equal the perimeter:

2 + x + sqrt(x^2 + 4) = 12

sqrt(x^2 + 4) = 12 - 2 - x = 10 - x

Square both sides:

x^2 + 4 = (10 - x)^2 = 100 - 20x + x^2

20x = 96 ==> x = 96/20 = 24/5 = 4.8 inches (answer)

The hypoteneuse is 12 - 2 - 4.8 = 5.2 inches (answer)

Check: 2^2 + 4.8^2 = 4 + 23.04 = 27.04 = 5.2^2 (okay)

Also, 2 + 4.8 + 5.2 = 12 (okay)

I think someone else got this answer too. If so, they're right.

Answer 4

In a right triangle a^2 + b^2 = c^2
In this triangle a+b+c=12 & a=2
2+b+c=12 or b+c=10 or b=10-c
4 + b^2 = c^2 or 4 + (10-c)^2 = c^2
so 4 + 100 - 20c +c^2 = c^2 or 104 - 20c = 0 or 20c=104
It means that c=5.2
b=10-c=10-5.2=4.8
Finally: a=2, b=4.8, c=5.2

Answer 5

concern is a million/2 base x top (which would be the two shorter aspects of a suitable angled triangle). Intuitively the utmost section must be while the two facets are equivalent (i.E. the two are 8 cms), making use of the analogy of a sq. being the utmost field for a given perimeter.

Answer 6

12 - 2 = 10
10/2 = 5
the 2 sides are both 5 cm