Question

Length of the rectangle is x cm and the diagonal of the rectangle is (x + 1) cm. Then the breadth of the rectangle is (x - 7) cm. Find the perimeter of the rectangle. (x ≠ 4)

• A. 36 cm
• B. 34 cm
• C. 32 cm
• D. 38 cm

Answer 1

Answer:

B. 34 cm

Solution: Solution: Length of the rectangle = x cm Diagonal of the rectangle = (x + 1) cm Breadth of the rectangle = (x - 7) cm (x + 1)2 = x2 + (x - 7)2 x2 + 1 + 2 × x × 1 = x2 + x2 + 49 - 2 × 7 × x x2 + 1 + 2x = 2x2 - 14x + 49 x2 - 16x + 48 = 0 x2 - 12x - 4x + 48 = 0 x( x - 12) - 4( x - 12) = 0 (x - 12) (x - 4) = 0 So value of x = 12 Length of the rectangle = 12 cm Breadth of the rectangle = 12 - 7 = 5cm Perimeter of the rectangle = 2 ( l + b) = 2 × ( 12 + 5) = 34 cm Hence, option(B) is correct.