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2 years ago

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The perimeter of a rectangle is 136 ft. The ratio of its length to its width is 9 : 8. What are the dimensions of the rectangle?

40 ft by 28 ft 44 ft by 24 ft 48 ft by 20 ft 36 ft by 32 ft

1 answer:

bezimeni [28]2 years ago

5 0

9: 8 = 9+8 = 17

136/17 = 8

8 * 9 = 72 / 2 = 36

8*8 = 64 / 2 = 32

32 +32 + 36 + 36 = 136

the rectangle is 36 x 32

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The areas of the two watch faces have a ratio of 16:25 What is the ratio of the radius of the smaller watch face to the radius o

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Answer:

The ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.

Step-by-step explanation:

Let the Area of smaller watch face be $A_1$

Also Let the Area of Larger watch face be $A_2$

Also Let the radius of smaller watch face be $r_1$

Also Let the radius of Larger watch face be $r_2$

Now given:

$\frac{A_1}{A_2} =\frac{16}{25}$

We need to find the ratio of the radius of the smaller watch face to the radius of the larger watch face.

Solution:

Since the watch face is in circular form.

Then we can say that;

Area of the circle is equal 'π' times square of the radius 'r'.

framing in equation form we get;

$A_1 = \pi {r_1}^2$

$A_2 = \pi {r_2}^2$

So we get;

$\frac{A_1}{A_2}= \frac{\pi {r_1}^2}{\pi {r_2}^2}$

Substituting the value we get;

$\frac{16}{25}= \frac{\pi {r_1}^2}{\pi {r_2}^2}$

Now 'π' from numerator and denominator gets cancelled.

$\frac{16}{25}= \frac{{r_1}^2}{{r_2}^2}$

Now Taking square roots on both side we get;

$\sqrt{\frac{16}{25}}= \sqrt{\frac{{r_1}^2}{{r_2}^2}}\\\\\frac{4}{5}= \frac{r_1}{r_2}$

Hence the ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.

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