contestada

A scale drawing of an office space uses a scale of 1 in : 4 yd. The scale drawing has an area of 12 square inches.The area of the office space is ____ square yards

Respuesta :

The scale factor of area of the drawing to the area of the office is the

square of the scale factor of the length of the drawing.

  • The area of the office space is 192 square yards.

Reasons:

The given parameters are;

1 inch in the scale drawing = 4 yd. in actual dimension

4 yd. = 144 inches

Therefore;

1 inch in the scale drawing = 144 inches in actual dimension

The scale factor of  length of the drawing, s = 1:144

The scale factor of area = s²

Therefore, we have;

  • [tex]\dfrac{Drawing \ area}{Actual \ area} =s^2[/tex]

Therefore, we have;

  • [tex]\dfrac{Drawing \ area}{Actual \ area} =\dfrac{12}{A} = s^2 = \left( \dfrac{1}{144} \right)^2[/tex]

Where;

A = The actual office space area

There fore;

12 × 144² = A × 1²

A = 12 × 144² = 248,832 in.²

1 yd.² = 1,296 in.²

  • [tex]248,832 \, in.^2 = \dfrac{248,832}{1,296} \, yd.^2 = 192 \, yd.^2[/tex]

The area of the office space is 192 square yards.

Lear more here:

https://brainly.com/question/17166840

Otras preguntas