A certain television is advertised as a 38-inch TV (the diagonal length). If the height of the TV is 25 inches, how wide is the TV? Round to the nearest tenth of an inch.
We can use the Pythagorean theorem to solve for the width of the TV, since we know the height and diagonal length. Let the width be x. Then, we have:
(25)^2 + x^2 = (38)^2
625 + x^2 = 1444
x^2 = 1444 - 625
x^2 = 819
x ≈ 28.6 inches (rounded to the nearest tenth)
Therefore, the TV is approximately 28.6 inches wide.
An altitude is drawn from the vertex of an isosceles triangle, forming a right angle and two congruent triangles. As a result, the altitude cuts the base into two equal segments. The length of the altitude is 13 inches, and the length of the base is 8 inches. Find the triangle’s perimeter. Round to the nearest tenth of an inch.
Since the altitude forms two congruent triangles, each of those triangles is a right triangle with one leg of length 4 (half the length of the base) and a hypotenuse of length 13. Using the Pythagorean theorem, we can solve for the other leg of each right triangle:
(leg)^2 + 4^2 = 13^2
(leg)^2 + 16 = 169
(leg)^2 = 153
(leg) ≈ 12.4
So each leg of the isosceles triangle has length approximately 12.4 inches. The perimeter of the triangle is then:
perimeter = 2(leg) + base
perimeter = 2(12.4) + 8
perimeter ≈ 32.8 inches (rounded to the nearest tenth)
Therefore, the perimeter of the triangle is approximately 32.8 inches.
To find the width of the TV, we can use the Pythagorean theorem.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Let's label the width of the TV as 'w'. So, we have:
w^2 + 25^2 = 38^2
w^2 + 625 = 1444
w^2 = 1444 - 625
w^2 = 819
w ≈ √819
w ≈ 28.6
So, the width of the TV is approximately 28.6 inches (rounded to the nearest tenth).