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If the diagonal of a rectangle is 5 cm and one of its sides is 4 cm, then its area is
- a)20 sq.cm
- b)12 sq.cm
- c)10 sq.cm
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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If the diagonal of a rectangle is 5 cm and one of its sides is 4 cm, t...
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Given:
- Diagonal of the rectangle = 5 cm
- One side of the rectangle = 4 cm
To find:
The area of the rectangle
Solution:
To find the area of the rectangle, we need to know the length and width of the rectangle. However, in this case, we are only given the diagonal and one side of the rectangle.
Using Pythagoras theorem:
According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
So, in this case, we can use the Pythagoras theorem to find the length of the other side of the rectangle.
Let the length of the rectangle be 'l' and the width be 'w'.
According to the Pythagoras theorem:
l² + w² = diagonal²
l² + 4² = 5²
l² + 16 = 25
l² = 25 - 16
l² = 9
l = √9
l = 3 cm
Calculating the area:
Now that we know the length and width of the rectangle, we can calculate its area using the formula:
Area = length * width
Area = 3 cm * 4 cm
Area = 12 sq.cm
Therefore, the area of the rectangle is 12 sq.cm, which corresponds to option 'B'.
- Diagonal of the rectangle = 5 cm
- One side of the rectangle = 4 cm
To find:
The area of the rectangle
Solution:
To find the area of the rectangle, we need to know the length and width of the rectangle. However, in this case, we are only given the diagonal and one side of the rectangle.
Using Pythagoras theorem:
According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
So, in this case, we can use the Pythagoras theorem to find the length of the other side of the rectangle.
Let the length of the rectangle be 'l' and the width be 'w'.
According to the Pythagoras theorem:
l² + w² = diagonal²
l² + 4² = 5²
l² + 16 = 25
l² = 25 - 16
l² = 9
l = √9
l = 3 cm
Calculating the area:
Now that we know the length and width of the rectangle, we can calculate its area using the formula:
Area = length * width
Area = 3 cm * 4 cm
Area = 12 sq.cm
Therefore, the area of the rectangle is 12 sq.cm, which corresponds to option 'B'.
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If the diagonal of a rectangle is 5 cm and one of its sides is 4 cm, then its area isa)20 sq.cmb)12 sq.cmc)10 sq.cmd)none of theseCorrect answer is option 'B'. Can you explain this answer?
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