Answer:
Both Scott and Tara have responded correctly.
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
A=(1/2)[b1+b2]h
we have
b1=16 cm
b2=24 cm
h=8 cm -----> <em>Note</em> The height is 8 cm instead of 18 cm
substitute
A=(1/2)[16+24](8)
A=160 cm²
<em>Verify Scott 's work</em>
<em>Note</em> Scott wrote A = (1/2)(24 + 16)(8) instead of A = 2(24 + 16)(8)
Remember that the Commutative Property establishes "The order of the addends does not alter its result"
so
(24+16)=(16+24)
A = (1/2)(24 + 16)(8)=160 cm²
<em>Verify Tara's work</em>
<em>Note</em> Tara wrote A = (1/2)(16+24)(8) instead of A = (16 + 24)(8)
A = (1/2)(16+24)(8)=160 cm²
3x + 4y = - 8
The equation of a line in standard form is Ax + By = C
where A is a positive integer and B, C are integers
Express the line in ' slope- intercept form '
y = mx + c → (m is the slope and c is the y-intercept)
here m = -
and c = - 2
hence y = -
x - 2 → equation in slope- intercept form
multiply all terms by 4
4y = - 3x - 8
add 3x to both sides
3x + 4y = - 8 → in standard form
Answer: 37 units
Step-by-step explanation:
This also works as the height of the triangle.
This also works as the base of the triangle.
Let's call pink ''a'', and blue ''b''. The side we're looking for ''c'' is the hypothenuse.
To find the values of a and b, use the area formula of a square and solve for a side. In this case, since we're going to need the squared values, this step can be omitted.

![s=\sqrt[]{A}](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%5D%7BA%7D)
Let's work with Blue.
![s=\sqrt[]{144units^2} \\s=12units](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%5D%7B144units%5E2%7D%20%5C%5Cs%3D12units)
Now Pink.
![s=\sqrt[]{1225units^2}\\s=35units](https://tex.z-dn.net/?f=s%3D%5Csqrt%5B%5D%7B1225units%5E2%7D%5C%5Cs%3D35units)
So we have a triangle with a base of 35 units and a height of 12 units.
Now let's use the pythagoream's theorem to solve.
![c^2=a^2+b^2\\c=\sqrt[]{a^2+b^2} \\c=\sqrt[]{(12units)^2+(35units)^2}\\c=\sqrt[]{144units^2+1225units^2}\\ c=\sqrt[]{1369units^2}\\ c=37units](https://tex.z-dn.net/?f=c%5E2%3Da%5E2%2Bb%5E2%5C%5Cc%3D%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%20%5C%5Cc%3D%5Csqrt%5B%5D%7B%2812units%29%5E2%2B%2835units%29%5E2%7D%5C%5Cc%3D%5Csqrt%5B%5D%7B144units%5E2%2B1225units%5E2%7D%5C%5C%20c%3D%5Csqrt%5B%5D%7B1369units%5E2%7D%5C%5C%20c%3D37units)
Answer: $23..50 see attachment for the explanation.