How do you find the area if only given a ratio and the width of a rectangle

Question

The width of a rectangle is 12 inches. The width to height ratio is 16:9. How do you find the area?

Answer 1

If the Width is 12 inches . lets say the height is h

Ratio of the Width and height is 16: 9

we can write 12 : h = 16 : 9

or we can write 12 / h = 16 / 9

multiplying both sides by h,

12 =( 16 / 9 ) * h

12* 9 = 16 h

dividing both sides by 16

12* 9 / 16 = h

h = 6.75

Now area of that rectangle is 12 * 6.75 = 81 square inch

Answer 2

Hi Wendy,

If you know that the width is 12 inches, and the width to height is 16:9, we can solve for the unknown side using the ratio of 12:x :: 16:9 Or another way of writing it, 12 is to x as 16 is to 9.

So, by answering "how much of 16 is 12" - or "12/16 = 0.75" we can know our scaling factor for the other side, so now we need 0.75 times 9, or 6.75

So now that we know the height is 6.75, we can find the area by taking 6.75 and multiplying it by the width of 12, getting 81 inches square.

If you'd like more help understanding some algebra and geometry concepts, feel free to contact me.