Question

what is the diagonal length of a rectangle having dimensions
$80cm \times 60cm$
​

Answer 1

Answer:

100 cm

Step-by-step explanation:

Let ABCD be the rectangle having dimensions 80 cm x 60 cm. Here,

• AB and DC are length.
• AD and BC are breadth.
• AC is the diagonal of the rectangle.

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Consider the ∆ ABC.

$\dashrightarrow \sf { AB = Hypotenuse }$

$\dashrightarrow \sf { AB = 80 cm }$

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$\dashrightarrow \sf { BC = Perpendicular }$

$\dashrightarrow \sf { BC = 60 cm }$

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$\dashrightarrow \sf { AC = Hypotenuse }$

$\dashrightarrow \sf { AC = ? \: \: cm}$

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According to pythagoras property,

• The square of hypotenuse or the square of the longest side of the right angled triangle is equivalent to the sum of the squares of the base and the perpendicular.

Applying pythagoras theorem,

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$\dashrightarrow \sf { H^2 = B^2 + P^2}$

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$\dashrightarrow \sf { (AC)^2 = (AB)^2 + (BC)^2}$

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$\dashrightarrow \sf { (AC)^2 = (80 \: cm)^2 + (60 \: cm)^2}$

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$\dashrightarrow \sf { (AC)^2 = 6400 \: cm^2 + 3600 \: cm^2}$

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$\dashrightarrow \sf { (AC)^2 = 10000 \: cm^2}$

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$\dashrightarrow \sf { AC =\sqrt{\Big \{ 10000 \: cm^2\Big\}} }$

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$\dashrightarrow \underline{\boxed{\sf { AC = 100 \: cm} }}$

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Therefore, diagonal of the rectangle having dimensions as 60 cm and 80 cm is 100 cm.

More Information :

• A rectangle is a quadrilateral having 4 vertices, 4 sides an 4 angles.

• Opposite sides of a rectangle are equal.

• Measure of each of its interior angle is 90°.

• Perimeter of a rectangle is equivalent to two times of the sum of its length and breadth.

• Area of a rectangle is equivalent to the product of its length and breadth.

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