The perimeter of a rectangle is 70 cm and its diagonal is 25cm. The area of the rectangle is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 300 cm2.
The perimeter of a rectangle = 70 cm
The diagonal of the rectangle = 25 cm
Let the length of the rectangle be a cm and the width be b cm.
So, 2(a + b) = 70
⇒ a + b = 70/2 = 35
⇒ b = 35 - a .....(1)
Also, a2 + b2 = 252 = 625 (using the Pythagorean theorem)
⇒ a2 + (35 - a)2 = 625
⇒ a2 + 1225 - 70a + a2 = 625
⇒ a2 - 35a + 300 = 0
⇒ (a - 15)(a - 20) = 0
⇒ a = 15 or 20
If a = 15, then b = 35 - 15 = 20
If a = 20, then b = 35 - 20 = 15
Thus, the length and width are 15 cm and 20 cm.
Area = Length × Breadth = a × b = 15 × 20 = 300 cm2
Therefore, the area of the rectangle is 300 cm2.