Question

a local businesses bought a square ploy of land. the sides of the lot measure 32 feet on each side. he decides to split the lot into two equal sized right triangles by putting a fence down the diagonal. approximately how many feet of fencing I'll he need?​

Answer 1

Approximate length of the diagonal fencing needed is 45.25 cm.

Explanation:

Here, each side of the square shaped land = 32 ft

Now, the diagonal fencing is made in side the plot so that the land is divided into two right triangles.

In the triangle:

Base side of the triangle = 32 cm

Perpendicular length of the triangle = 32 cm

Let us assume the hypotenuse of the triangle = k cm

⇒The length of the diagonal in the square = k cm

by PYTHAGORAS THEOREM in a right angled triangle:

`(Base)^(2) +  (Perpendicular)^(2)  =  (Hypotenuse)^(2)`

⇒
`(32)^2 + (32)^2  =k^2\\or, k^2  = 1024 + 1024 =  2048\\\implies k = √(2048)  = 45.25`

or, k = 45.25 cm

Hence,the approximate length of the diagonal fencing needed to fence the square land is 45.25 cm.