Mathematics: The area of a square is numerically 45 more than the perimeter. find the length of the side

The area of a square is numerically 45 more than

Ответ:

rmusungu4

17.01.2022

Area of square = l²
Perimeter of square = 4l

According to the question,
$l^2 = 45 + 4l \\\\ l^2 - 4l - 45 = 0 \\\\ l^2 -9l+5l-45=0 \\\\ l(l-9)+5(l-9) =0 \\\\(l-9)(l+5)=0$

Using zero product property,

Either,
$l-9 = 0 \\
~~~~~~l = 9$

Or,
$l+5=0 \\
~~~~~~l=-5$

Since length can't be negative, the length is 9

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Ответ:

ghadeeraljelawy

07.12.2022

Mathematics

Because ∠PTS and ∠QTR are vertical angles, we can use the Vertical Angle Theorem to say they are equal. Therefore:

11(y - 10) = (4y - 5)

Now, solve for y:

11y - 110 = 4y - 5

7y = 105

y = 15

You got up to here, but rather than finding the angle measure they asked for, you put the value of y. So, lets do that. Plug y back into ∠PTS:

11(y - 10)

=11(15 - 10)

=11(5)

=55

Therefore, the measurement of ∠PTS is 55°.

Hope this helps! :)

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The area of a square is numerically 45 more than the perimeter. find the length of the side

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