Saturday

April 19, 2014

April 19, 2014

Posted by **Nabil** on Monday, October 10, 2011 at 12:06am.

Each piece bent into a square.

Find the length of the two pieces so the sum of the areas of the two squares in 10 square inches.

- algebra -
**Anonymous**, Monday, October 10, 2011 at 2:01amL = Length of a wire

x = Length of the first pice

y = Length of the cecond pice

x / 4 = Length of the first square

y / 4 = Length of the second square

L = 16 in

16 = x + y

y = 16 - x

Area of the first pice = ( x / 4 ) ^ 2

Area of the second pice = ( y / 4 ) ^ 2

( x / 4 ) ^ 2 + ( y / 4 ) ^ 2 = 10

x ^ 2 / 16 + y ^ 2 / 16 = 10

( x ^ 2 + y ^ 2 ) / 16 = 10 Multiply both sides with 16

x ^ 2 + y ^ 2 = 160

x ^ 2 + ( 16 - x ) ^ 2 = 160

( Remark: ( 16 - x ) ^ 2 = 16 ^ 2 - 32 x + x ^ 2

x ^ 2 + 16 ^ 2 - 32 x + x ^ 2 = 160

2 x ^ 2 + 256 - 32 x = 160

2 x ^ 2 + 256 - 160 - 32 x = 0

2 x ^ 2 + 96 - 32 x = 0

2 x ^ 2 - 32 x + 96 = 0 Divide both sides with 2

x ^ 2 - 16 x + 48 = 0

The exact solutions are:

x = 12

and

x = 4

Length of a wire = 16 in

y = 16 - x

When: x = 12 ; y = 16 - 12 = 4

When x = 4 ; y = 16 - 4 = 12

Length of the two pieces :

12 in

and

4 in

Proof:

( 12 / 4 ) ^ 2 + ( 4 / 4 ) ^ 2 = 10

3 ^ 2 + 1 ^ 2 = 10

9 + 1 = 10 in ^ 2

P.S.

If you don know how to solve equation:

x ^ 2 - 16 x + 48 = 0

In google type:

quadratic equation online

When you see list of results click on:

Free Online Quadratic Equation Solver:Solve by Quadratic Formula

When page be open in rectangle type:

x ^ 2 - 16 x + 48 = 0

and click option:

solve it!

You wil see solution step-by-step

**Related Questions**

Calc - A wire 100 inches long is to be cut into two pieces. One of the pieces ...

math - A florist uses wire frames to support flower arrangements displayed at ...

math - Juan buys 18 meter of wire. He cuts the wire into pieces of 3 meters long...

Math word problem - I know the answer, but is there a formula to show work? Amy ...

Calculus - A piece of wire 40 m long is cut into two pieces. One piece is bent ...

algebra - a 3 1/2 foot piece of rope is cut into two pieces. one of these pieces...

math - wire is cut into 2 pieces with one piece 14 feet shorter than other.The ...

math - A wire 320 in. long is cut into two pieces. One piece is formed into a ...

Calculus - A wire 4 meters long is cut into two pieces. One piece is bent into a...

Math - 12 pieces each 13 3/8 inches long need to be cut from a board 16 feet ...