Answer:
C
Step-by-step explanation:
Hi there!
We're given a rectangle with one side marked as 16 and another marked as 12
We need to find the length of the diagonal
Rectangles have a property that makes the opposite sides congruent. Therefore, the side opposite to the side marked as 16 is also 16 and the side opposite to the side marked as 12 is also 12 because of that property.
Now let's look at the shapes cut by the diagonal; they are right triangles.
We only need to look at one of the triangles for this problem
The measures of 12 and 16 in the triangle are the legs (sides that make up the right angle) and the diagonal is the hypotenuse (the side that is opposite to the right angle).
You can absolutely solve for the diagonal/hypotenuse by doing Pythagorean theorem, but there's a shortcut:
3, 4, 5 is a common Pythagorean triple
(3²+4²=5²)
(9+16=25)
(25=25)
You may notice that dividing 12 and 16 by 4 are equal to 3 and 4 respectively
that means it's a 3, 4, 5 triangle, just by multiplied 4
So that means the hypotenuse has to be 5 * 4, which is equal to 20 inches
Therefore the answer is C
Hope this helps!
