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Ludmilka [50]
3 years ago
12

Any help on this ? 30 pts

Mathematics
1 answer:
Vlad1618 [11]3 years ago
6 0
The perimeter is adding up all sides of a shape. Here we are told that the perimeter of the triangle is 41 inches. So we can make the equation:

\sf x+3x+7y=41

Combine like terms(x + 3x = 4x):

\sf 4x+7y=41

We are also told that the perimeter of the rectangle is 66 inches. The formula for the perimeter of a rectangle is:

\sf P=2(l+w)

Plug in what we know:

\sf 66=2(3x+7y)

Distribute 2 into the parenthesis:

\sf 6x+14y=66

So our system of equations is:

\sf 4x+7y=41
\sf 6x+14y=66

Let's use the substitution method to solve this system. Let's solve for 'x' in the second equation:

\sf 6x+14y=66

Subtract 14y to both sides:

\sf 6x=-14y+66

Divide 6 to both sides:

\sf x=-\dfrac{7}{3}y+11

Now let's plug this in for 'x' in the first equation:

\sf 4x+7y=41

\sf 4(-\dfrac{7}{3}y+11)+7y=41

Distribute:

\sf -\dfrac{28}{3}y+44+7y=41

Combine like terms:

\sf -\dfrac{7}{3}y+44=41

Subtract 44 to both sides:

\sf -\dfrac{7}{3}y=-3

Divide -7/3 to both sides or multiply by its reciprocal -3/7:

\sf y=\dfrac{9}{7}

So the solution to the system of equations is:

\sf (8,\dfrac{9}{7})

Plug these values in to find the length and width of the rectangle.

Length:

\sf 3x

\sf 3(8)

\boxed{\sf 24}

Width:

\sf 7y

\sf 7(\dfrac{9}{7})

\boxed{\sf 9}
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