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2 years ago

The length of a rectangle is 3 cm longer than its width.

Mathematics

1 answer:

pochemuha2 years ago

7 0

Answer:

108 cm²

Step-by-step explanation:

Area of a rectangle, A = length, l × width, w

Perimeter of a rectangle = (2 × length) + (2 × width)

42 cm = 2l + 2w

but length = w + 3cm

42 cm = 2(w + 3cm) + 2w

42 cm = 2w + 6cm + 2w

42 cm = 6cm + 4w

4w = (42 - 6) cm

4w = 36 cm

》w = 9cm

》l = w + 3cm = 9cm + 3cm

l = 12 cm

Area = 12 × 9 = 108 cm²

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Determine whether each expression is equivalent to

larisa [96]

The algebraic expressions, $x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$ and $5x + 3$ are equivalent to $2x + 4y - 5 + 3x + 8 - 4y$

To determine whether each expression is equivalent to $2x + 4y - 5 + 3x + 8 - 4y$ , apply the knowledge of algebra to solve each of the following in it's simplest form.

First, simplify $2x + 4y - 5 + 3x + 8 - 4y$ as follows:

Add like terms

$2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y - 5 + 8\\5x + 3$

Next, compare or simplify where necessary each of the given algebraic expressions with $5x + 3$

First Option

$x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$

Add like terms together

$2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y -5+8\\5x + 3$

Therefore, $x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$ is equivalent to $2x + 4y - 5 + 3x + 8 - 4y$

Check the box for YES.

Second Option:

$6xy + 3 - 4y$ (cannot be simplified further)

$6xy + 3 - 4y\neq 2x + 4y - 5 + 3x + 8 - 4y$

Therefore:

Leave the box BLANK for NO.

Third Option:

$-8y + 5x - 3$ (cannot be simplified further)

$-8y + 5x - 3 \neq 2x + 4y -5 + 3x + 8 - 4y$

Therefore:

Leave the box BLANK for NO.

Fourth Option:

$5x + 3$

$5x + 3 = 2x + 4y - 5 + 3x + 8 - 4y$

Therefore:

Check the box for YES.

Thus, the algebraic expressions that are equivalent to $2x + 4y - 5 + 3x + 8 - 4y$ are:

$x + x + y + y + y + y - 5 + x + x + x + 8 - 4y$

$5x + 3$

Learn more about algebraic expressions here:

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