word problem help please!

Question

A holding pen for cattle must be square and have a diagonal length of 110 meters.
a. Find the length of a side of the pen.
b. Find the area of the pen.

Answer 1

So, the reason a triangle has an area of bh/2 is because it's half a rectangle. Draw a diagonal across a square and you have to right angles.

 

a² + b² = 110²

 

Hey, since it's a square, a and b are the same.

 

2a² = 12,100

a² = 6050

a = √6050 = 77.78 m

 

The area is given above, 6050 m².

 

Answer 2

 

 x^2 + x^2 = 110^2

 

2*x^2 = 12100

 

x^2 = 6050 <----- THIS IS THE AREA

 

x = 77.78 <---- THIS IS THE MEASURE OF EACH SIDE

 

The exact value is the square root of

6050

 

= sqrt(50 x 121)  = sqrt(5 x 2 x 5 x 11 x 11)

 

                            = 11 * 5 * sqrt(2)

 

                           = 55*Sqrt(2)