Question

the length of one of the diagonals of a rhombus is 5 cm less than the length of the Other diagonal the area of the Rhombus is 33 cm square find the length of each diagonal​

Answer 1

Answer:

length of diagonals are 11cm and 6cm

Step-by-step explanation:

area of rhombus = (1/2)* product of its diagonals

let x cm be one diagonal and thus other diagonal will be x-5cm

area=(1/2)*x*(x-5)

33=(1/2)*(x²-5x)

x²-5x=66

x²-5x-66=0

x²-11x+6x-66=0

x(x-11)+6(x-11)=0

(x+6)(x-11)=0

x=11 cm. (because diagonal cannot be negative -6cm)

two diagonals are 11cm and 6cm

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.