Question

Rectangle ABCD is similar to rectangle WXYZ. What is the value of AB if WX is & feet, AD is 12 feet, and WZ is 16 feet?

Answer 1

Answer:

Similar rectangles states that the corresponding sides are in proportion.

As per the statement:

Rectangle ABCD is similar to rectangle WXYZ.

WX = 8 feet, AD = 12 feet and WZ = 16 feet.

Since. Rectangle ABCD and rectangle WXYZ are similar

then;

their corresponding sides are in proportion:

$\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}$

To find the value of AB:

$\frac{AB}{WX}=\frac{AD}{WZ}$

Substitute the given values we have;

$\frac{AB}{8}=\frac{12}{16}$

Multiply both sides by 8 we have;

$AB = \frac{12}{16} \times 8 = \frac{96}{16}=6$

Therefore, the value of AB is 6 units.