Question

ABCD is a rectangle in which AC = 15cm and angle ACD = theta. find the area of rectangle if tan theta = 3/4.​

Answer 1

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ABCD a rectangle ABCD and join AC

Now, in triangle ACD, AC = 15 cm

Angle ACD = theta

and tan theta = 3/4

Now, tan theta = tan (ACD) = AD/CD

So, AD = 3x and CD = 4x

Now, in triangle ACD

AC² = AD² = CD²

==>AC² = (3x)² + (4x)² = 9x² + 16² = 25x²

==>AC² = 25x²

==>AC = 5x

Also AC = 15cm

So, AC = 5x = 15cm

==>5x = 15

==>x = 3cm

Now AD = 3x = 3×3 = 9cm

DC = 4x = 4×3 = 12cm

• Area of Rectangle = length × breadth = AD × DC = 9×12 = 108cm²

hope it helps

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