Question

If you were constructing a TRIANGULAR FRAME, and you had wood in the length of 4 inches, 4 inches, and 7 inches, would it make a triangle? Would you be able to create a frame from these pieces of wood?

Answer 1

Answer: The answer is 'YES'.

Step-by-step explanation:  Given that we are constructing a TRIANGULAR FRAME with pieces of wood having lengths 4 inches, 4 inches and 7 inches. We are to check if it is possible to create the frame with these pieces.

Let AB, BC and CA be the three sides of the triangle ABC made of wood pieces, where

AB = 4 in, BC = 4 in and CA = 7 inch.

Now, to make a triangle, the sum of any two sides must be greater than the third side.

We have

AB + BC = 4 + 4 = 8 > CA,

BC + CA = 4 + 7 = 11 > AB

and

CA + AB = 7 + 4 = 11 > BC.

Thus, we can easily make the triangular frame with the given pieces of wood. Also, since AB = BC, so the frame will be in the form of an isosceles triangle. Please see the attached figure.

Answer 2

Answer: Yes it is possible to construct a triangle and it will be an isosceles triangle.

Step-by-step explanation:

The triangle inequality says that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side.

The given sides of the triangle is 4 inches, 4 inches, and 7 inches.

Here,

$4+4=8>7\\7+4>4$

So by triangle inequality, a triangle with sides   4 inches, 4 inches, and 7 inches. is possible.

Since it has two equal sides as 4 inches , then it must be an isosceles triangle.