Finding the Rectangle Diagonal Length
To find the length of the diagonal of a rectangle, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In a rectangle, the length, width, and diagonal form a right-angled triangle.
Applying the Pythagorean Theorem
Let the length of the rectangle be '$l$' and the width be '$w$'. Let the diagonal be '$d$'. According to the Pythagorean theorem:
$d^2 = l^2 + w^2$
Calculating the Diagonal
Given:
- Length, $l = 9$ cm
- Width, $w = 5$ cm
Substitute the values into the formula:
$d^2 = 9^2 + 5^2$
$d^2 = 81 + 25$
$d^2 = 106$
To find the diagonal '$d$', take the square root of both sides:
$d = \sqrt{106}$
Since length must be a positive value, we only consider the positive square root.
Conclusion
The length of the diagonal is $\sqrt{106}$ cm.
Similar Questions
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Important Questions from 2-D Mensuration
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Calculate the area of the triangle whose sides are 8 cm, 9 cm and 13 cm. (Rounded up to two decimal places)
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