In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the perimeter of the rectangle ABCD.

Given: cot ∠ ABD = 1.5 = cot ∠ ABD = ∴ If length of AB = 3x cm, length of AD = 2x cm. In Δ ABD, ⇒ BD2 = AB2 \+ AD2 (∵ BD is hypotenuse) ⇒ BD2 = (3x)2 \+ (2x)2 ⇒ BD2 = 9x2 \+ 4x2 ⇒ BD2 = 13x2 ⇒ BD = ⇒ BD = x It is given that BD = 26 cm So, x = 26 ⇒ x = ⇒ x = ⇒ x = ⇒ x = AB = DC = 3x = 3 x = cm and AD = BC = 2 x = cm Perimeter of rectangle ABCD = sum of all sides of rectangle = AB \+ BC \+ CD \+ DA = cm = cm Area of rectangle = length x breadth = AB x BC = cm2 = 24 13 cm2 = 312 cm2 Hence, area of rectangle = 312 cm2 and perimeter = cm.

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Mathematics

In rectangle ABCD, diagonal BD = 26 cm and cotangent of angle ABD = 1.5. Find the area and the perimeter of the rectangle ABCD.

Trigonometric Identities

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