Maths-
General
Easy
Question
A framed television has a ratio of width to height of about 1.732 : 1. For a television of height h inches, what is an equivalent expression for the length of the diagonal? Justify your answer. Write an expression for parimeter.
The correct answer is: Length of the diagonal for the given framed tv is 2h units where h is its height and its perimeter can be expressed in terms of its height as- 5.5h units2
Hint:-
1. By Pythagorean theorem, for a right angled triangle-
(Hypotenuse)2 = Sum of the squares of other 2 sides …..................... (Where Hypotenuse is the side opposite to the right angle)
2. Perimeter of a rectangle = 2 (length + breadth)
Step-by-step solution:-
Let the length, width, height and diagonal for the given framed tv be l, w, h & d, respectively.
From the given information, we get-
Width / Height = 1.732 / 1
∴ 1 (Width) = 1.732 (Height)
∴ Width = 1.732 × Height
∴ w = 1.732 h ….................................................... (Equation i)
Now, from the adjacent diagram, we can observe that-
Diagonal cuts the framed tv into 2 triangles with a right angle (as edges of a rectangle form right angle)
∴ using Pythagorean theorem, we get-
(Diagonal)2 = (Width)2 + (Height)2
∴ d2 = (1.732 h)2 + h2 .................................................... (From Equation i)
∴ d2 = 3h2 + h2
∴ d2 = 4h2
∴ d = 2h ........................................................................ (Taking square roots both the sides)
Perimeter of the given framed tv = 2 (width + height)
∴ Perimeter of the given framed tv = 2 (1.732h + h) ................. (From Equation i)
∴ Perimeter of the given framed tv = 2 × 2.732h
∴ Perimeter of the given framed tv ≈ 5.5 h units2.
Final Answer:-
∴ Length of the diagonal for the given framed tv is 2h units where h is its height and its perimeter can be expressed in terms of its height as- 5.5h units2.
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