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The sides of a triangle having area 7776 sq. cm are in the ratio 3 : 4 : 5. The perimeter of the triangle is (SSC CGL 1st Sit. 2015)
- a)400 cm
- b)412 cm
- c)424 cm
- d)432 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The sides of a triangle having area 7776 sq. cm are in the ratio 3 : 4...
Let sides of Δ be 3x, 4x, 5x
7776 = 6x2
∴ x = 36
Sides of Δ will be 108, 144 and 180
Perimeter of Δ is 108 +144 + 180 = 432 cm
7776 = 6x2
∴ x = 36
Sides of Δ will be 108, 144 and 180
Perimeter of Δ is 108 +144 + 180 = 432 cm
Most Upvoted Answer
The sides of a triangle having area 7776 sq. cm are in the ratio 3 : 4...
Understanding Triangle Area and Ratios
To find the perimeter of a triangle with an area of 7776 sq. cm and sides in the ratio 3:4:5, we first need to determine the lengths of the sides.
Step 1: Assigning Side Lengths
Let the sides of the triangle be:
- 3x (first side)
- 4x (second side)
- 5x (third side)
Step 2: Area of the Triangle
Since the triangle is a right triangle (3:4:5 ratio), we can use the formula for the area:
Area = (1/2) * base * height
Here, base = 4x and height = 3x.
Thus, the area can be calculated as:
Area = (1/2) * 4x * 3x = 6x^2
We know the area is 7776 sq. cm, so we set up the equation:
6x^2 = 7776
Step 3: Solving for x
To find x, divide both sides by 6:
x^2 = 1296
Now, take the square root of both sides:
x = 36
Step 4: Finding the Sides
Now, substitute x back to find the lengths of each side:
- First side = 3x = 3 * 36 = 108 cm
- Second side = 4x = 4 * 36 = 144 cm
- Third side = 5x = 5 * 36 = 180 cm
Step 5: Calculating the Perimeter
The perimeter (P) of the triangle is the sum of all sides:
P = 108 + 144 + 180 = 432 cm
Conclusion
Thus, the perimeter of the triangle is 432 cm, which corresponds to option 'D'.
To find the perimeter of a triangle with an area of 7776 sq. cm and sides in the ratio 3:4:5, we first need to determine the lengths of the sides.
Step 1: Assigning Side Lengths
Let the sides of the triangle be:
- 3x (first side)
- 4x (second side)
- 5x (third side)
Step 2: Area of the Triangle
Since the triangle is a right triangle (3:4:5 ratio), we can use the formula for the area:
Area = (1/2) * base * height
Here, base = 4x and height = 3x.
Thus, the area can be calculated as:
Area = (1/2) * 4x * 3x = 6x^2
We know the area is 7776 sq. cm, so we set up the equation:
6x^2 = 7776
Step 3: Solving for x
To find x, divide both sides by 6:
x^2 = 1296
Now, take the square root of both sides:
x = 36
Step 4: Finding the Sides
Now, substitute x back to find the lengths of each side:
- First side = 3x = 3 * 36 = 108 cm
- Second side = 4x = 4 * 36 = 144 cm
- Third side = 5x = 5 * 36 = 180 cm
Step 5: Calculating the Perimeter
The perimeter (P) of the triangle is the sum of all sides:
P = 108 + 144 + 180 = 432 cm
Conclusion
Thus, the perimeter of the triangle is 432 cm, which corresponds to option 'D'.
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Community Answer
The sides of a triangle having area 7776 sq. cm are in the ratio 3 : 4...
Let sides of Δ be 3x, 4x, 5x
7776 = 6x2
∴ x = 36
Sides of Δ will be 108, 144 and 180
Perimeter of Δ is 108 +144 + 180 = 432 cm
7776 = 6x2
∴ x = 36
Sides of Δ will be 108, 144 and 180
Perimeter of Δ is 108 +144 + 180 = 432 cm
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The sides of a triangle having area 7776 sq. cm are in the ratio 3 : 4 : 5. The perimeter of the triangle is (SSC CGL 1st Sit. 2015)a)400 cmb)412 cmc)424 cmd)432 cmCorrect answer is option 'D'. Can you explain this answer?
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