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The base of a right-angled triangle is 12 cm and the difference between the other two sides is 6 cm. What will be the perimeter of the triangle?
Correct answer is '36'. Can you explain this answer?
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The base of a right-angled triangle is 12 cm and the difference betwe...
Given
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Base = 12 cm
P2 + b2 = h2
Let height be x cm
So, hypotenous is (x + 6)cm
(x + 6)2 − x2 = 144
⇒ x2 + 36 + 12x − x2 = 144
⇒12x =108
x = 9
Height = 9 cm
So, hypotenuse is 15 cm
Perimeter = 9 + 12 + 15
= 36 cm
∴ The perimeter of the triangle is 36 cm.
Hence, the correct answer is 36 cm.
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The base of a right-angled triangle is 12 cm and the difference betwe...
Understanding the Problem
To find the perimeter of the right-angled triangle, we know:
- Base (b) = 12 cm
- Difference between the other two sides (hypotenuse and perpendicular) = 6 cm
Let’s denote:
- Perpendicular side = a
- Base side = b = 12 cm
- Hypotenuse = c
Given that c - a = 6, we can express the hypotenuse as:
- c = a + 6
Using the Pythagorean Theorem
According to the Pythagorean theorem, for a right-angled triangle:
- a² + b² = c²
Substituting the known values:
- a² + 12² = (a + 6)²
Expanding the equation:
- a² + 144 = a² + 12a + 36
This simplifies to:
- 144 = 12a + 36
Solving for 'a'
Rearranging gives:
- 12a = 144 - 36
- 12a = 108
- a = 9 cm
Now substituting a back to find c:
- c = a + 6 = 9 + 6 = 15 cm
Calculating the Perimeter
The perimeter (P) of the triangle is the sum of all sides:
- P = a + b + c
- P = 9 cm + 12 cm + 15 cm
Therefore:
- P = 36 cm
Final Answer
The perimeter of the triangle is 36 cm.
To find the perimeter of the right-angled triangle, we know:
- Base (b) = 12 cm
- Difference between the other two sides (hypotenuse and perpendicular) = 6 cm
Let’s denote:
- Perpendicular side = a
- Base side = b = 12 cm
- Hypotenuse = c
Given that c - a = 6, we can express the hypotenuse as:
- c = a + 6
Using the Pythagorean Theorem
According to the Pythagorean theorem, for a right-angled triangle:
- a² + b² = c²
Substituting the known values:
- a² + 12² = (a + 6)²
Expanding the equation:
- a² + 144 = a² + 12a + 36
This simplifies to:
- 144 = 12a + 36
Solving for 'a'
Rearranging gives:
- 12a = 144 - 36
- 12a = 108
- a = 9 cm
Now substituting a back to find c:
- c = a + 6 = 9 + 6 = 15 cm
Calculating the Perimeter
The perimeter (P) of the triangle is the sum of all sides:
- P = a + b + c
- P = 9 cm + 12 cm + 15 cm
Therefore:
- P = 36 cm
Final Answer
The perimeter of the triangle is 36 cm.
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The base of a right-angled triangle is 12 cm and the difference between the other two sides is 6 cm. What will be the perimeter of the triangle?Correct answer is '36'. Can you explain this answer?
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