The polygons are similar, but not necessarily drawn to scale. Find the value of x.

Question

Bigger polygon: 53 and x
Smaller polygon: 8 and 2

In quadrilateral ABCD, AE=x+14 and BE=3x-18. For what value of x is ABCD a rectangle?
A. 30
B. 16
C. 20
D. 18

Please help!!

Answer 1

To determine the value of x for the first problem, we can set up a proportion using the corresponding sides of the similar polygons:

53/8 = x/2

Cross multiplying, we get:

8x = 106
x = 13.25

So, the value of x is 13.25.

Now, for the second problem, we know that in a rectangle, opposite sides are equal and perpendicular to each other. This means that AE and BE must be equal for ABCD to be a rectangle.

Setting up the equation:

x + 14 = 3x - 18
14 + 18 = 3x - x
32 = 2x
x = 16

Therefore, for ABCD to be a rectangle, the value of x must be 16. So, the answer is:

B. 16