Answer:
m+5=7
Step-by-step explanation:
The equations we get are
l = 6 + 2w (We get this from "The length of the rectangle is 6 more than 2 times the width.")
and
2l + 2w = 140 (We get this from the perimeter. Two times the length plus two times the width equals the perimeter of a quadrilateral.)
The first equation can be written as
l - 2w = 6
So now we have
2l + 2w = 140
l - 2w = 6
____________
Add the two equations.
We get 3l = 146
Divide by 3 on both sides.
l =
48
Your answer is
48
.
Solving a system of linear equations, we conclude that the measure of side Z is 2√13
<h3>How to find the measure of side Z?</h3>
Remember the Pythagorean theorem. It says that the square of the hypotenuse is equal to the sum of the squares of the legs.
In the image, we can identify 3 right triangles, and with the Pythagorean theorem, we can write a system of 3 equations.
x^2 = y^2 + 4^2
z^2 = y^2 + 9^2
(4 + 9)^2 = z^2 + x^2
We want to solve that for z.
Now, the second equation can be rewritten to:
y^2 = z^2 - 9^2
Now let's replace the first equation into the third one, so we get:
(4 + 9)^2 = z^2 + (y^2 + 4^2)
Now we can replace y^2 by z^2 - 9^2
(4 + 9)^2 = z^2 + ((z^2 - 9^2) + 4^2)
Now we can solve this:
(13)^2 = z^2 + z^2 - 9^2 + 4^2
(13)^2 + 9^2 - 4^2 = 2*z^2
104/2 = z^2
52 = z^2
√52 = z
√(4*13) = z
√4*√13 = z
2√13 = z
We conclude that the measure of side Z is 2√13
If you want to learn more about systems of equations:
brainly.com/question/13729904
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You’re answer should be 60