Question

The length of one of the diagonals of a rhombus is greater than another by 5cm .it's area is 18sq.cm. find the length of the diagonals of the rhombus

Answer 1

Answer:

length of the diagonals of the rhombus are 4 cm  and 9 cm

Step-by-step explanation:

let one of the diagonal is x

another diagonal is x+5

Area of the rhombus is 18 sq cm

Area of the rhombus when the diagonals are given is

$A= \frac{p q}{2} \\18=\frac{x\times (x+5)}{2} \\x\times (x+5)=36\\x^2+5x-36= 0$

by solving this equation

$x^2+9x-4x-36=0\\x(x+9)-4(x+9) =0\\(x+9)(x-4) =0$

we get x = -9 or x =4

here we have to take positive value

x= 4

other diagonal is  =4+5 = 9 cm

length of the diagonals of the rhombus are 4 cm  and 9 cm