Question

the length of one of the diagnol of a rhombus is 5 cm less than the other diagnol . The area of the rhombus is 33 cm square . Find the length of each diagnol .

ANSWER = 6 CM and 11 CM
but explain step by step​

Answer 1

$\huge\boxed{\fcolorbox{black}{pink}{ANSWER..}}$

Where p and q are the diagonals of the rhombus. Let the length of one of the diagonals is x. Then the length of another diagonal is x-5. The area is 33 cm².

Answer 2

$\huge\boxed{\fcolorbox{black}{red}{ANSWER..}}$

The length of each diagonal is 11 cm and 6 cm.

Consider the provided information.

Area of rhombus is: A=$\frac{pq}{2}$

Where p and q are the diagonals of the rhombus.

Let the length of one of the diagonals is x.

Then the length of another diagonal is x-5.

The area is 33 cm².

Substitute the respective values in the above formula.

33=$\frac{(x)(x-5)}{2}$

x²-5x=66x²−5x=66

x²-5x-66=0x² −5x−66=0

x²-11x+6x-66=0x² −11x+6x−66=0

x(x-11)+6(x-11)=0x(x−11)+6(x−11)=0

(x-11)(x+6)=0(x−11)(x+6)=0

x=11\ or\ x=-6x=11 or x=−6

The value of length can't be a negative number.

Hence, the length of one diagonal is 11 cm.

The length of another diagonal is 5 less than 11.

11-5 = 6cm

Hence, the length of each diagonal is 11 cm and 6 cm.