The lengths of adjacent sides of the parallelogram are 40 cm and 50 cm.
<h3>What is a parallelogram?</h3>
A parallelogram is a simple quadrilateral with two pairs of parallel sides.
Now, suppose a and be are two sides of parallelogram
Then, Perimeter P = 2( a+ b)
Now, it is given that perimeter of a parallelogram is 180 cm.
⇒ 2( a+ b) = 180
⇒ a + b = 90
It is also given that one side exceeds the other by 10 cm.
⇒ a = b + 10
Putting the value of a in above equation we get,
b + 10 + b = 90
⇒ 2b = 90 - 10
⇒ 2b = 80
⇒ b = 40 cm
Similarly, a = b + 10
⇒ a = 40 + 10
⇒ a = 50 cm
Hence, the required sides of parallelogram are 40cm and 50cm.
More about parallelogram:
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Let's use Gaussian elimination. Consider the augmented matrix,
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C-1%20%26%202%20%26%203%20%26%200%20%26%201%20%26%200%5C%5C1%20%26%201%20%26%204%20%26%200%20%26%200%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add row 1 to row 2, and add -1 (row 1) to row 3:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%202%20%26%201%20%26%201%20%26%200%5C%5C0%20%26%202%20%26%205%20%26%20-1%20%26%200%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add -2 (row 2) to row 3:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%202%20%26%201%20%26%201%20%26%200%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add -2 (row 3) to row 2:
![\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%20-1%20%26%20-1%20%26%201%20%26%200%20%26%200%5C%5C0%20%26%201%20%26%200%20%26%207%20%26%205%20%26%20-2%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
• Add row 2 and row 3 to row 1:
![\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Cccc%7D1%20%26%200%20%26%200%20%26%205%20%26%203%20%26%20-1%5C%5C0%20%26%201%20%26%200%20%26%207%20%26%205%20%26%20-2%5C%5C0%20%26%200%20%26%201%20%26%20-3%20%26%20-2%20%26%201%5Cend%7Barray%7D%5Cright%5D)
So the inverse is

.............................
Answer: 112 7th graders ride the bus .
Step-by-step explanation:
Given: The proportion of 7th graders ride the bus to school= 35% = 0.35 [to remove % we divide number by 100]
If there are 320 seventh graders, then the number of 7th graders ride the bus = 320 x (proportion of 7th graders ride the bus to school)


Hence, 112 7th graders ride the bus .