If the perimeter of the large square tile is 48 inches and the perimeter of the smaller square is 16 inches, what is the perimeter of one of the trapezoids? a 19.7 inches b 25.4 inches c 27.3 inches d 32 inches

Answer:

The perimeter of one of the trapezoids is equal to 27.3 inches

Step-by-step explanation:

Given:

Perimeter of the large square tile = 48 inches

Perimeter of the smaller square = 16 inches

To Find :

The perimeter of one of the trapezoids

see the attached figure to better understand the problem

Solution:

we know that

The perimeter of a square is

P =

step 1:Find the length side of the smaller square

step 2  :Find the length side of the large square

step 3: Find the height of one trapezoid

The height is equal to

=4 in

step 4: Find the hypotenuse of one isosceles right triangle

one trapezoid is equal to one square and two isosceles right triangles.

Applying Pythagoras Theorem

step 5: Find the perimeter of one of the trapezoid

The perimeter is equal to

P = 16 +8(1.414)

P= 16 + 11.28

P= 27.28

P =27.3

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x