Question

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?

Answer 1

Answer:

The perimeter of one of the trapezoids is equal to $(16+8\sqrt{2})\ in$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The perimeter of a square is

$P=4b$

where

b is the length side of the square

step 1

Find the length side of the smaller square

$16=4b$

$b=16/4=4\ in$

step 2

Find the length side of the large square

$48=4b$

$b=48/4=12\ in$

step 3

Find the height of one trapezoid

The height is equal to

$h=(12-4)/2=4\ in$

step 4

Remember that in this problem, one trapezoid is equal to one square plus two isosceles right triangles.

Find the hypotenuse of one isosceles right triangle

Applying Pythagoras Theorem

$c^{2}=4^{2} +4^{2} \\ \\c=4\sqrt{2}\ in$

step 5

Find the perimeter of one of the trapezoid

The perimeter is equal to

$P=(4\sqrt{2} +4+4\sqrt{2}+12)\\ \\P=(16+8\sqrt{2})\ in$

Answer 2

Answer:

27.3 Inches

Step-by-step explanation: