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kap26 [50]
2 years ago
13

A decorative window is made up of a rectangle with semicircles at either end. The ratio of AD to AB is 3:2 and AB is 30 inches.

What is the ratio of the area of the rectangle to the combined area of the semicircles?
PLS HELP ME QUICK, I HAVE TO BE DONE BY 3!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics
1 answer:
scZoUnD [109]2 years ago
8 0

Answer: The required ratio will be

84:1034

Step-by-step explanation:

Since we have given that

Ratio of AD to AB is 3:2

Length of AB = 30 inches

So, it becomes

2x=30\\\\x=\frac{30}{2}=15\ inches

So, Length of AD becomes

3x=3\times 15=45\ inches

Now, at either end , there is a semicircle.

Radius of semicircle along AB is given by

\frac{30}{2}=15\ inches

So, Area of semicircle along AB and CD is given by

2\times \frac{\pi r^2}{2}\\\\=\frac{22}{7}\times 15\times 15\\\\=\frac{4950}{7}\ in^2

Radius of semicircle along AD is given by

\frac{45}{2}=22.5\ inches

Area of semicircle along AD and BC is given by

2\times \frac{1}{2}\pi r^2\\\\=\frac{22}{7}\times \frac{45}{2}\times \frac{45}{2}\\\\=\frac{445500}{28}\ in^2

And the combined area of the semicircles is given by

\frac{4950}{7}+\frac{445500}{28}\\\\=\frac{465300}{28}\ in^2

Area of rectangle is given by

Length\times width\\\\=AD\times AB\\\\=45\times 30\\\\=1350\ in^2

Hence, Ratio of the area of the rectangle to the combined area of the semicircles is given by

1350:\frac{465300}{28}\\\\=1350\times 28:465300\\\\=37800:465300\\\\=84:1034

Hence, the required ratio will be

84:1034

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