ABCD is a rectangle, if AC is 2(x-3) and BD is X+5 what are the lengths of the diagnoals?
a. 2,2
b. 11,11
c. -3,-3
d. 16,16
In any rectangle the diagonals are equal, so .....
2(x-3) = x+5
2x - 6 = x+5
x = 11
subbing into either one gets us 16
so the choice is d)
abcd is a rectangle . find the lenght of each diagonal .
ac=2(x-3)
bd= x+5
16,16
16
if ABCD is a rectangle in which AC=2x-3 and BD=x+5 then the value of x is
To find the lengths of the diagonals of a rectangle, we need to use the properties of rectangles.
First, let's analyze the given information. We are given that AC is 2(x-3) and BD is X+5. These represent the lengths of the two diagonals.
Since ABCD is a rectangle, opposite sides are congruent. Therefore, we can say that AC is equal to BD.
Setting the two expressions for AC and BD equal to each other, we have:
2(x-3) = x+5
Now, let's solve for x:
2x - 6 = x + 5
x - 6 = 5
x = 11
Now that we have found the value of x, we can substitute it back into one of the expressions to find the lengths of the diagonals:
AC = 2(x-3)
AC = 2(11-3)
AC = 2(8)
AC = 16
BD = x + 5
BD = 11 + 5
BD = 16
So, the lengths of the diagonals are both 16.
Therefore, the correct answer is option D: 16, 16.