Question

quilt squares are cut on the diagonal to form triangular quilt pieces. the hypotenuse of the resulting triangles is 16 inches long.what is the side of each piece. A.8in B.8and 3 in C.16and 2in D. 8and2in.

Answer 1

The right triangle formed is shown below

From the diagram,

x represents the side of the square. Recall that a square has equal sides

To find x, we would apply the pythagorean theorem which is expressed as

hypotenuse^2 = one leg^2 + other leg^2

From the diagram,

hypotenuse = 16

one leg = other leg = x

By substituting these values into the formula,

16^2 = x^2 + x^2

16^2 = 2x^2

256 = 2x^2

Dividing both sides by 2,

2x^2/2 = 256/2

x^2 = 128

Taking square root of both sides, we have

`\begin{gathered} x\text{ = }\sqrt[]{128}\text{ = }\sqrt[]{2*64}\text{ = }\sqrt[]{2}\text{ }*\text{ }\sqrt[]{64} \\ x\text{ = 8}\sqrt[]{2} \end{gathered}`

The correct option is 8√2 in