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The sides of a right-angled triangle forming right angle are in the ratio 5 : 12. If the area of the triangle is 270 cm2, then the length of the hypotenuse is
- a)39 cm
- b)42 cm
- c)45 cm
- d)51 cm
Correct answer is option 'A'. Can you explain this answer?
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The sides of a right-angled triangle forming right angle are in the ra...
Given data-
Sides of a right-angled triangle forming right angle are in the ratio 5 : 12
Let sides of triangle forming right angle be 5x & 12x respectively, where x is constant of proportionality.
Area of the triangle = ½ × base × height = ½ × 5x × 12x = 30x2
30x2 = 270
⇒ x2 = 9
⇒ x = 3
∴ sides of triangle forming right angle are-
5x = 5 × 3 = 15 cm
& 12x = 12 × 3 = 36 cm
Using Pythagoras theorem
hypotenuse2 = 152 + 362
⇒ hypotenuse2 = 225 + 1296
⇒ hypotenuse2 = 1521
∴ Hypotenuse = √1521 = 39 cm
Sides of a right-angled triangle forming right angle are in the ratio 5 : 12
Let sides of triangle forming right angle be 5x & 12x respectively, where x is constant of proportionality.
Area of the triangle = ½ × base × height = ½ × 5x × 12x = 30x2
30x2 = 270
⇒ x2 = 9
⇒ x = 3
∴ sides of triangle forming right angle are-
5x = 5 × 3 = 15 cm
& 12x = 12 × 3 = 36 cm
Using Pythagoras theorem
hypotenuse2 = 152 + 362
⇒ hypotenuse2 = 225 + 1296
⇒ hypotenuse2 = 1521
∴ Hypotenuse = √1521 = 39 cm
Most Upvoted Answer
The sides of a right-angled triangle forming right angle are in the ra...
Solution:
Let the sides of the right-angled triangle be 5x, 12x, and hypotenuse be h.
The area of a right-angled triangle is given by the formula:
Area = (1/2) * base * height
In this case, the base is 5x and the height is 12x. So, we can write the area as:
270 = (1/2) * 5x * 12x
Simplifying this equation, we get:
270 = 30x^2
Dividing both sides by 30, we get:
9 = x^2
Taking the square root of both sides, we get:
x = √9
x = 3
So, the sides of the triangle are 5x = 5 * 3 = 15 and 12x = 12 * 3 = 36.
Now, we can use the Pythagorean theorem to find the length of the hypotenuse.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Using this theorem, we can write the equation:
h^2 = 15^2 + 36^2
Simplifying this equation, we get:
h^2 = 225 + 1296
h^2 = 1521
Taking the square root of both sides, we get:
h = √1521
h = 39
Therefore, the length of the hypotenuse is 39 cm.
Hence, the correct answer is option 'A'.
Let the sides of the right-angled triangle be 5x, 12x, and hypotenuse be h.
The area of a right-angled triangle is given by the formula:
Area = (1/2) * base * height
In this case, the base is 5x and the height is 12x. So, we can write the area as:
270 = (1/2) * 5x * 12x
Simplifying this equation, we get:
270 = 30x^2
Dividing both sides by 30, we get:
9 = x^2
Taking the square root of both sides, we get:
x = √9
x = 3
So, the sides of the triangle are 5x = 5 * 3 = 15 and 12x = 12 * 3 = 36.
Now, we can use the Pythagorean theorem to find the length of the hypotenuse.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Using this theorem, we can write the equation:
h^2 = 15^2 + 36^2
Simplifying this equation, we get:
h^2 = 225 + 1296
h^2 = 1521
Taking the square root of both sides, we get:
h = √1521
h = 39
Therefore, the length of the hypotenuse is 39 cm.
Hence, the correct answer is option 'A'.
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The sides of a right-angled triangle forming right angle are in the ratio 5 : 12. If the area of the triangle is 270 cm2, then the length of the hypotenuse isa)39 cmb)42 cmc)45 cmd)51 cmCorrect answer is option 'A'. Can you explain this answer?
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