Answer:
The horizontal length is 80 cm, and the vertical height is 60 cm.
Step-by-step explanation:
The aspect ratio is the ratio of the horizontal length to the vertical height.
We have a rectangle with sides 4 and 3. We can find the length of the diagonal.
We can use the Pythagorean theorem to find the length of the diagonal.
a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
c^2 = 25
c = 5
The diagonal is 5 in the ratio.
The ratio of the horizontal length to the vertical height to the diagonal is
4:3:5
We multiply all the numbers in the ratio by the same unknown, x.
A ratio of 4:3:5 is the same as a ratio of 4x:3x:5x.
We are told that the diagonal is 100 cm, so we have
4x : 3x : 100,
but we already had a ratio of
4x : 3x : 5x, so
5x = 100, and we can find x.
5x = 100
Divide both sides by 5.
x = 20
Since x = 20, then the horizontal length 4x = 4(20) = 80,
and the vertical height 3x = 3(20) = 60
Answer: The horizontal length is 80 cm, and the vertical height is 60 cm.
