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The ratio of two smaller sides of a right-angled triangle is 4 : 3, A rectangle is on the largest side of the triangle in such a way that largest side will be the length of the rectangle. The breadth of rectangle is four fifth of its length. Find the length of shortest side of triangle if the perimetre of rectangle is 1.8 m.
  • a)
    60 cm
  • b)
    40 cm
  • c)
    15 cm
  • d)
    30 cm
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The ratio of two smaller sides of a right-angled triangle is 4 : 3, A ...
Given information:
- Ratio of two smaller sides of a right-angled triangle is 4:3
- A rectangle is on the largest side of the triangle in such a way that largest side will be the length of the rectangle
- Breadth of rectangle is four-fifths of its length
- Perimeter of rectangle is 1.8 m

To find: Length of shortest side of triangle

Solution:
Let the two smaller sides of the right-angled triangle be 4x and 3x.
Using Pythagoras theorem, the largest side (hypotenuse) can be found as:
(hypotenuse)^2 = (4x)^2 + (3x)^2
(hypotenuse)^2 = 16x^2 + 9x^2
(hypotenuse)^2 = 25x^2
hypotenuse = 5x

Let the length of the rectangle be 5x (same as hypotenuse)
Then the breadth of the rectangle is (4/5) * 5x = 4x

Perimeter of rectangle = 2(length + breadth)
1.8 = 2(5x + 4x)
1.8 = 2(9x)
1.8 = 18x
x = 0.1

Therefore, the two smaller sides of the triangle are:
4x = 4(0.1) = 0.4 m
3x = 3(0.1) = 0.3 m

And the length of the hypotenuse (largest side) is:
5x = 5(0.1) = 0.5 m

Therefore, the correct answer is option 'D' - 30 cm.
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The ratio of two smaller sides of a right-angled triangle is 4 : 3, A rectangle is on the largest side of the triangle in such a way that largest side will be the length of the rectangle. The breadth of rectangle is four fifth of its length. Find the length of shortest side of triangle if the perimetre of rectangle is 1.8 m.a)60 cmb)40 cmc)15 cmd)30 cmCorrect answer is option 'D'. Can you explain this answer?
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