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ella [17]
2 years ago
12

a school is building a square shed that is 5 meters long on each side however before the construction begins school management d

ecides to halve the length of the shed on all sides by how much would the area of the square shed decrease?
Mathematics
1 answer:
nadezda [96]2 years ago
7 0
It would decrease 2.5
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Please Help! Thanks!
svetlana [45]

Answer:

C, 20 units

Step-by-step explanation:

We see that both angles QRS and QTR are 90 degrees. In addition, angles SQR and RQT are equivalent (because they're both angle Q).

By AA Similarity, we know that triangle QTR is similar to triangle QRS.

With this similarity in mind, we can look at the ratios of corresponding lengths to set up a proportion. QR from triangle QTR is the hypotenuse, and it corresponds to hypotenuse QS from triangle QRS. So, we can write the ratio x/(9 + 16) = x/25.

Now, we see that long leg QT of triangle QTR corresponds to long leg QR of triangle QRS. So, another ratio we can write is: 16/x.

Finally, we set these two ratios equal to each other:

\frac{x}{25} =\frac{16}{x}

Cross-multiplying, we get: x^{2} =16*25=400.

Thus, x = \sqrt{400} =20. The answer is C, 20 units.

Hope this helps!

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3 years ago
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