Maths-
General
Easy
Question
Write an expression in simplest form for the missing side length. Then find the side lengths of each triangle to the nearest tenth when x=15.
The correct answer is: Length of the missing side can be expressed as- 4√2 x. Also, when x = 15, length of all of the sides of the triangle are 30ft, 90ft and 60√2 ft
Hint:-
In a right angled triangle, the square of the hypotenuse (side opposite to the right angle) is equal to the sum of the squares of the remaining 2 sides.
"Step-by-step solution:-
Let the missing side be y units.
From the given diagram, we observe that-
The given triangle is a right angled triangle and we need to find expression for the length of its missing side i.e. y.
Using the Pythagorean theorem, we get-
(6x)2 = (2x)2 + (y)2
∴ 36x2 = 4x2 + y2
∴ 36x2 - 4x2 = y2 ............................................. (Taking all x variables together)
∴ 32x2 = y2
∴ √(32x2) = y ............................................. (Taking square root both the sides)
∴ √(2 × 2 × 2 × 2 × 2 × x × x) = y ............................................. (Factorizing radical)
∴ √(2 × 2) × √(2 × 2) × √2 × √(x × x) = y ............................................. [Product property- √m × √n = √(mn)]
∴ √(2)2 × √(2)2 × √2 × √(x)2 = y
∴ (2)2/2× (2)2/2 × √2 × (x)2/2 = y ...................... [Power rule- m√(bn) = b n/m]
∴ (2)1 × (2)1 × √2 × (x)1 = y
∴ 2 × 2 × √2 × x = y
∴ 4√2 x = y
When x = 15,
Length of side 1 = 2x = 2 × 15 = 30 ft
Length of side 2 = 4√2 x = 4√2 × 15 = 60√2 ft
Length of Hypotenuse = 6x = 6 × 15 = 90 ft
Final Answer:-
∴ Length of the missing side can be expressed as- 4√2 x. Also, when x = 15, length of all of the sides of the triangle are 30ft, 90ft and 60√2 ft.
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