The Design for a Mural is 16 in. Wide and 9 in High. What are the Dimensions of the largest possible complete mural that can be painted on a wall 24 ft wide by 14 ft wide?

And Can you Please Explain.
I understood how to do it. but which height or width will fill the space first? And Why

12 inch=1ft

24x12 =288
14x12=168

To find the largest possible complete mural that can be painted on a wall with dimensions 24 ft wide by 14 ft high, we need to determine whether the width or height of the mural will fill the space first.

First, let's convert the dimensions of the mural to feet. The design is 16 in. wide, which is equivalent to 16/12 = 1.33 ft, and 9 in. high, which is equivalent to 9/12 = 0.75 ft.

To determine whether the width or height will fill the space first, we can divide the wall dimensions by the mural dimensions:

For the width: 24 ft ÷ 1.33 ft = 18.05,
For the height: 14 ft ÷ 0.75 ft = 18.67.

Since 18.05 is smaller than 18.67, it means the width of the mural will fill the available space first.

Therefore, the dimensions of the largest possible complete mural that can be painted on the wall will be 24 ft wide and (1.33 ft × 14 ft)/24 ft = 0.78 ft high.

find the area of the triangle

6yd and 2ft

well, the wall's height is 14/9 times the mural's height

the wall's width is 24/16 times the mural's width.

So, which ratio is larger?

14/9 > 24/16

so, as the mural is scaled up, the sides will fill the width before the top and bottom fill the height.