Consider the figure.
find ab if bc = 3, bd = 5, and ad = 5.
ab= ?

In right angled triangle ΔBCD we have:

Using the Pythagorean Theorem we have:

But as a length of a side can't be negative.

Hence, we have:

Also, In right angled triangle ΔBCA using the Pythagorean Theorem we have:

( Since, on taking square root on both the side we have negative or positive term but the length of a side can't be negative.

Hence, we took answer as a positive value)

Hence, we have:

c.

step-by-step explanation:

she should of added 9^2 and 12^2. that is because it is a^2+b^2=c^2. c^2 is the hypotenuse and should always be bigger than the other two numbers. which is why she should of added 9 squared and 12 squared together instead of 15 squared.

proportions are fractions that equal to each other. so if two fractions are the same, they are proportional.

let's check the answers to see if they are proportional.

question a is not proportional because you can't turn 1.5/3 to 3/9. if you try to multiply 1.5/3 by 2 or 3, you wont get 3/9. it's impossible to make the fractions the same.

question b is not proportional because you can't turn 22/33 to 4/6. 33 can't go into 6.

question c is proportional because when you multiply 2 and 3 by 71, you would get 142/213, and those fractions equal to each other

question d is proportional because when you divide 14 and 7 by 2, you would end up with 7/3.5, and those fractions equal to each other.