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The area of a right-angled triangle is two-third of the area of a rectangle. The base of triangle is 80% of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm. What is the height of the triangle?
- a)20 cm
- b)30 cm
- c)15 cm
- d)Can’t be determined
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The area of a right-angled triangle is two-third of the area of a rec...
1/2 × b × h = 2/3 × L × B
again,
b = 0.8B
2(L + B) = 200
height cannot be calculated by given conditions.
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The area of a right-angled triangle is two-third of the area of a rec...
To solve this problem, let's assume the base of the right-angled triangle is 'b' cm and the breadth of the rectangle is 'B' cm.
According to the given information, the base of the triangle is 80% of the breadth of the rectangle. So, we have:
b = 0.8B
Let's also assume the height of the triangle is 'h' cm and the length of the rectangle is 'L' cm.
We know that the area of a right-angled triangle is given by the formula:
Area of triangle = (1/2) * base * height
And the area of a rectangle is given by the formula:
Area of rectangle = length * breadth
According to the question, the area of the triangle is two-thirds of the area of the rectangle. So, we can write the equation as:
(1/2) * b * h = (2/3) * L * B
Simplifying the equation, we get:
b * h = (4/3) * L * B
Substituting the value of b from the first equation, we get:
0.8B * h = (4/3) * L * B
Simplifying further, we get:
h = (4/3) * L * (1/0.8)
h = (4/3) * L * (5/4)
h = (5/3) * L
Now, let's consider the perimeter of the rectangle. The perimeter is the sum of all the sides, which is given by the formula:
Perimeter of rectangle = 2 * (length + breadth)
According to the question, the perimeter of the rectangle is 200 cm. So, we can write the equation as:
2 * (L + B) = 200
Simplifying the equation, we get:
L + B = 100
Now, substituting the value of B from the first equation, we get:
L + 0.8B = 100
L + 0.8(1.25h) = 100
L + h = 100
From this equation, we can see that the height of the triangle cannot be determined. Hence, the correct answer is option 'D' (Can't be determined).
According to the given information, the base of the triangle is 80% of the breadth of the rectangle. So, we have:
b = 0.8B
Let's also assume the height of the triangle is 'h' cm and the length of the rectangle is 'L' cm.
We know that the area of a right-angled triangle is given by the formula:
Area of triangle = (1/2) * base * height
And the area of a rectangle is given by the formula:
Area of rectangle = length * breadth
According to the question, the area of the triangle is two-thirds of the area of the rectangle. So, we can write the equation as:
(1/2) * b * h = (2/3) * L * B
Simplifying the equation, we get:
b * h = (4/3) * L * B
Substituting the value of b from the first equation, we get:
0.8B * h = (4/3) * L * B
Simplifying further, we get:
h = (4/3) * L * (1/0.8)
h = (4/3) * L * (5/4)
h = (5/3) * L
Now, let's consider the perimeter of the rectangle. The perimeter is the sum of all the sides, which is given by the formula:
Perimeter of rectangle = 2 * (length + breadth)
According to the question, the perimeter of the rectangle is 200 cm. So, we can write the equation as:
2 * (L + B) = 200
Simplifying the equation, we get:
L + B = 100
Now, substituting the value of B from the first equation, we get:
L + 0.8B = 100
L + 0.8(1.25h) = 100
L + h = 100
From this equation, we can see that the height of the triangle cannot be determined. Hence, the correct answer is option 'D' (Can't be determined).
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The area of a right-angled triangle is two-third of the area of a rectangle. The base of triangle is 80% of the breadth of the rectangle. If the perimeter of the rectangle is 200 cm. What is the height of the triangle?a)20 cmb)30 cmc)15 cmd)Can’t be determinedCorrect answer is option 'D'. Can you explain this answer?
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