Question

The perimeter of parallelogram ABCD is 46 inches. What is DA?

Answer 1

First we have 8x -5=3x+10, so x =3.
Hence AB =CD =19.
So 38+DA +BC =46, but DA =BC,
38+2DA=46, then 2DA =8,
DA =4.

Answer 2

Answer:  he correct option is B and the length of DA is 46 inches.

Explanation:

It is given that ABCD is a parallelogram with perimeter 46 inches.

Let the length of DA be x.

According to the property of parallelogram the length of opposite sides are equal.

The sides AB and DC are opposite sides. So,

$AB=DC$

$8x-5=3x+10$

$5x=15$

$x=5$

The value of x is 5. Therefore the length of AB is,

$AB=8x-5=8(3)-5=19$

The sides AD and BC are opposite sides, the length of AD and BC are equal.

Perimeter of a parallelogram is the sum of all side lengths.

$perimeter=AB+BC+CD+DA$

$46=2(AB)+2(AD)$

$46=2(19)+2(AD)$

$8=2(AD)$

$4=AD$

Therefore the value of AD is 4 inches and the correct option is B.