Question

a length of rectangle is less by 1 than 3 times its breadth. If the length of the diagonal is 37 cm , then find the length and breadth of rectangle​

Answer 1

Given info : A length of rectangle is less by 1 than 3 times its breadth. If the length of the diagonal is 37 cm.

To find : The length and breadth of rectangle are ...

solution : let breadth of rectangle is x

then length of rectangle= 3x - 1

∵ diagonal of rectangle = √(length² + breadth²)

⇒37 = √{(3x - 1)² + x² }

⇒37² = 9x² - 6x + 1 + x²

⇒1369 = 10x² - 6x + 1

⇒10x² - 6x - 1368 = 0

⇒5x² - 3x - 684 = 0

⇒5x² - 60x + 57x - 684 = 0

⇒(x - 12)(5x + 57) = 0

⇒x = 12 , x ≠ -57/12 because x is breadth so can't be negative.

now length = 3 × 12 - 1 = 35

Therefore the length and breadth of rectangle are 35 and 12 respectively.