Question

Tasha assembled a picture frame that is advertised as rectangular. The completed frame is 14 inches long and 10 inches wide. She measured the diagonal length across the frame as 20 inches. Which best explains why the frame cannot actually be rectangular?
14 squared + 10 squared not-equals 20 squared
14 + 10 not-equals 20
(14 + 10) squared not-equals 20 squared
(14 squared + 10 squared) squared not-equals 20 squared

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

Answer:

The frame cannot actually be rectangular is 14 squared + 10 squared not-equals 20 squared.

Step-by-step explanation:

A Pythagoras theorem states that:

If a triangle ABC is with AC it forms a hypotenuse and angle B which will form a 90 degree. It will be:

$| AC|^{2}$ = $| AB|^{2}$ +$|B|^{2}$

Here |AB| is the length of segment of the line AB.

According to Pythagoras theorem if a triangle cannot satisfy this theorem then, the angles will not measure 90 degrees.

Let us now understand that,

• When the rectangle has its sides which are perpendicular to each other.
• Let one side be a unit length.
• Let other adjacent side be length b .
• Let the diagonals be made to connect the ends of two perpendicular sides be the length of d units.

Now it becomes,

$D^{2} = a^{2} +b^{2}$

Given that:

Let us take,

A= 14 inches

B= 10 inches

D = 20 inches

Adding these values in the above equation, we get,

$D^{2} = 20^{2} = 400$

$a^{2} +b^{2} = 14^{2} +10^{2} =296$

Therefore, $d^{2}$ is not equal to $a^{2} + b^{2}$

Hence it is not supporting a rectangle.

#SPJ2