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3 years ago

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

Mathematics

2 answers:

kvv77 [185]3 years ago

5 0

I hope this helps you

Mekhanik [1.2K]3 years ago

5 0

ANSWER

$DA = 4inches$

EXPLANATION

The perimeter of a parallelogram is given by the formula,

$perimeter = 2w + 2l$

It is the same as that of the rectangle.

We were given that the perimeter is 46 inches. So now we need to determine the length of the parallelogram using the equation

$8 x - 5 = 3x + 10$
The reason is that, the opposite sides of a parallelogram are equal.

We solve the equation for x to obtain,

$8x - 3x = 10 + 5$

This means that,

$5x = 15$

Dividing through by 5, we obtain,

$x = 3inches$

Meaning the length is

$3(3) + 10 = 19inches$

We now plug in

$l=19,perimeter=46$

into

$perimeter = 2w + 2l$

to get,

$46= 2w+ 2 \times 19$

$46= 2w+ 38$

$46 - 38= 2w$

$8= 2w$

$4= w$

DA is the width of the parallelogram, therefore
$DA = 4inches$

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