jose wants to buy a new tv that will fit the opening of his entertainment center. the height of the opening in his entertainment center is 27 inches. usually, the opening of an entertainment center has a width-to-height ratio of 4:3.
what is the diagonal measurement of the opening in jose's entertainment center?
a^2+b^2=c^2
27^2+36^2=c^2
729+1296=c^2
2025=c^2
√2025=45
The diagonal measurement of the opening of Jose's entertainment center is 45 inches squared
width = (4/3)* 27 = 36
D^2 = 27^2 + 36^2
usk
To find the diagonal measurement of the opening in Jose's entertainment center, we can use the Pythagorean theorem, which states that the square of the hypotenuse (in this case, the diagonal measurement) is equal to the sum of the squares of the other two sides.
Let's assume the width of the opening is "x" inches. Given that the ratio of the width to height is 4:3, we can set up the following equation:
x / 27 = 4 / 3
To solve for "x," we can cross-multiply:
3x = 4 * 27
3x = 108
Dividing both sides by 3:
x = 36
So, the width of the opening in Jose's entertainment center is 36 inches.
Now, we can use the Pythagorean theorem to find the diagonal measurement. Let's call the diagonal "d":
d² = (36)² + (27)²
d² = 1296 + 729
d² = 2025
Taking the square root of both sides:
d = √2025
d ≈ 45
Therefore, the diagonal measurement of the opening in Jose's entertainment center is approximately 45 inches.