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strojnjashka [21]
3 years ago
8

if we increased one side of a square by 5 units and decreased the other by 3 units the area of the resulting rectangle would be

21 units squared greater than the area of the square how long are the sides of the original square
Mathematics
1 answer:
zvonat [6]3 years ago
3 0

Answer:

18 units

Step-by-step explanation:

So let's list out the sides.

for the first square let's just call them x

for the second square then they would be x+5 and x-3

So let's write out their areas we will cal the area of the first one z

x*x = z

(x+5)*(x-3) = z+21

since z = x^2 we can set up the second equation as a quadratic.

(x+5)*(x-3) = x^2 + 21

x^2 - 3x + 5x - 15 = x^2 + 21

But look, the x^2s cancel out

2x - 15 = 21

2x = 36

x = 18

Test it out and see if it fits the description, And if you don't understand anything just let me know so I can explain more.  

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Step 1

Use the ratio of the number to the percentage to get the required answer.

\frac{Total\text{ number of students}}{\text{The required number of students}}=\frac{Total\text{ percentage of the class}}{\text{Given percentage}}

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Step 2

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\begin{gathered} \frac{24}{x}=\frac{100}{78} \\ 100x=24\times78 \\ 100x=1872 \\ \frac{100x}{100}=\frac{1872}{100} \\ x=\text{ 18.72} \\ \text{Hence} \\ x\approx19students\text{ rounded to a whole number } \end{gathered}

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