Question

a door frame that appears to be rectangular has a height of 21 in, width of 20 in, and one diagonal that measures 29 in.
is the door frame rectangular?
show your work here
hint: to add the square root symbol ($\sqrt{\square}$), type
oot\

Explanation:

Step1: Apply Pythagorean theorem

For a rectangle, the diagonal $d$ should satisfy $d^2 = h^2 + w^2$, where $h=21$ in, $w=20$ in.
Calculate $h^2 + w^2$:
$21^2 + 20^2 = 441 + 400$

Step2: Sum the squared values

$441 + 400 = 841$

Step3: Calculate square of given diagonal

Given diagonal is 29 in, so $29^2 = 841$

Step4: Compare the two results

Since $21^2 + 20^2 = 29^2$, the frame satisfies the Pythagorean theorem for right angles.

Answer:

Yes, the door frame is rectangular.