Question

A rectangular tile has a thin diagonal line drawn in its design. The longer dimension of the tile is 12 inches. The angle formed by the diagonal and the shorter side of the tile is 72°. What is the perimeter of the tile? Enter your answer, rounded to the nearest inch, in the box.

Answer 1

Answer: 32 inches

Step-by-step explanation:

Since all the interior angles in a rectangle are right angles.

Therefore, the triangle which is formed by the diagonal and the shorter side of the tile with the longer side will be right triangle.

By trigonometry, in right triangle

$\tan{\theta}=\frac{\text{side opposite to }\theta}{\text{side adjacent to }\theta}$

let x be the smaller side.

Therefore,

$\tan72^{\circ}=\frac{12}{x}\\\Rightarrow\ 3.077683=\frac{12}{x}\\\Rightarrow\ x=12\times3.077683\\\Rightarrow\ x=3.89903703533\approx4\ inches$

The perimeter of the rectangular tile= $2(12+4)=2(16)=32\ inches$