Question

the length of one of the diagonals of a rhombus is 5 cm less than the lenght of the other diagonal .the area of the rhombus is 33 cm sq. . find the length of each diagonal .​

Answer 1

Answer:

11 cm & 6 cm

Step-by-step explanation:

area of rhombus =1/2×product of its diagonals

33=1/2×(x)×(x-5)

33×2=x (x-5)

66=x(x-5)

66=11 (11-5)

66=11×6

length of diagonals=11&6

Answer 2

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

Step-by-step explanation:

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.

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

$x^2-5x=66$

$x^2-5x-66=0$

$x^2-11x+6x-66=0$

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

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

$x=11\ or\ x=-6$

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.

#Learn more

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The lenght of one diagonal of a rhombus is less than the second diagonal by 4cm.thearea of the rhombus is 30 sq. cm. find the length of the diagonals