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The sides of an equilateral triangle are shortened by 12 units 13 units and 14 units respectively and a right angle triangle is formed. The side of the equilateral triangle is
- a)17 units
- b)16 units
- c)15 units
- d)18 units
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The sides of an equilateral triangle are shortened by 12 units 13 unit...
Given information:
- An equilateral triangle is shortened by 12 units, 13 units, and 14 units respectively.
- A right-angled triangle is formed from the shortened sides.
To find:
- The side of the equilateral triangle.
Solution:
Let the side of the equilateral triangle be 'x' units.
After shortening,
- The first side of the triangle becomes x - 12 units.
- The second side becomes x - 13 units.
- The third side becomes x - 14 units.
Using the Pythagorean theorem, we can say that:
(x - 12)^2 + (x - 13)^2 = (x - 14)^2
On solving this equation, we get:
x = 17 units
Therefore, the side of the equilateral triangle is 17 units.
Answer: Option A (17 units)
- An equilateral triangle is shortened by 12 units, 13 units, and 14 units respectively.
- A right-angled triangle is formed from the shortened sides.
To find:
- The side of the equilateral triangle.
Solution:
Let the side of the equilateral triangle be 'x' units.
After shortening,
- The first side of the triangle becomes x - 12 units.
- The second side becomes x - 13 units.
- The third side becomes x - 14 units.
Using the Pythagorean theorem, we can say that:
(x - 12)^2 + (x - 13)^2 = (x - 14)^2
On solving this equation, we get:
x = 17 units
Therefore, the side of the equilateral triangle is 17 units.
Answer: Option A (17 units)
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Community Answer
The sides of an equilateral triangle are shortened by 12 units 13 unit...
New sides of new Δ=x-12; x-13; x-14.
(x-12) side is the longest side in the right angled Δ
ACCORDING TO THE PYTHAGORAS THEORAM
(x-13)² + (x-14)²= (X-12)²
after opening the brackets...
x² + 169 - 26x + x² + 196 - 28x = x² + 144 - 24x
2x² + 365 - 54x = x² + 144 -24x
2x²- x² + 365 - 144 - 54x + 24x= 0
x² - 30x + 221 =0
x² -17x -13x + 221=0
x(x-17) -13(x-17)= 0
(x-13)(x-17)=0
x-13=0 or x-17=0
x=13 x=17
x ≠13 (because if x is 13 then side (x-13) of Δ would be zero
which is imposiible)
x= 17 units
(x-12) side is the longest side in the right angled Δ
ACCORDING TO THE PYTHAGORAS THEORAM
(x-13)² + (x-14)²= (X-12)²
after opening the brackets...
x² + 169 - 26x + x² + 196 - 28x = x² + 144 - 24x
2x² + 365 - 54x = x² + 144 -24x
2x²- x² + 365 - 144 - 54x + 24x= 0
x² - 30x + 221 =0
x² -17x -13x + 221=0
x(x-17) -13(x-17)= 0
(x-13)(x-17)=0
x-13=0 or x-17=0
x=13 x=17
x ≠13 (because if x is 13 then side (x-13) of Δ would be zero
which is imposiible)
x= 17 units
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The sides of an equilateral triangle are shortened by 12 units 13 units and 14 units respectively and a right angle triangle is formed. The side of the equilateral triangle isa)17 unitsb)16 unitsc)15 unitsd)18 unitsCorrect answer is option 'A'. Can you explain this answer?
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