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Agata [3.3K]
3 years ago
14

2) The two rectangles shown are similar.

Mathematics
1 answer:
Citrus2011 [14]3 years ago
5 0

Answer:

6\ cm

Step-by-step explanation:

First Rectangle:

length(l_1)=24\ cm\\\\Width(b_1)=9\ cm

Second Rectangle:

length(l_2)=16\ cm\\\\Let\ Width=b_2\ cm

Since\ these\ two\ rectangles\ are\ similar\\\\\frac{l_2}{l_1}=\frac{b_2}{b_1}\\\\\frac{16}{24}=\frac{b_2}{9}\\\\16\times 9=24\times b_2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ cross\ multiplication\\\\b_2=\frac{16\times 9}{24}\\\\b_2=6\ cm

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SOLUTION:

PQR is a right-angle triangle.

Therefore, to solve this problem, we will use Pythagoras theorem which is only applicable to right-angle triangles.

Pythagoras theorem is as displayed below:

a^2 + b^2 = c^2

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Where a and b = other two sides of right-angle triangle

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b = 13.8564...

b = 13.86 ( to 2 decimal places )

FINAL ANSWER:

Therefore, the length of QR is 13.86 centimetres to 2 decimal places.

Hope this helps! :)
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