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. Find the length of each diagonal. rhombus​

Answer 1

Step-by-step explanation:

let say x is one diagonal then other will be x+5

here x is the smaller one

so area of the rhombus =1/2(d1*d2)

1/2(x*(x+5))=33

x(x+5)=66

x^2+5x-66=0

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

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

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

so x=-11 and x= 6

so length can't be negatives so x=6

so lengths of the diagonals

x=6

x+5=6+5=11

Answer 2

Answer:

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

Step-by-step explanation:

Consider the provided information.

Area of rhombus is:  

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.

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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.