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3 years ago

The area of a square is 121 square inches. what is the length of a side

Mathematics

1 answer:

Agata [3.3K]3 years ago

4 0

The length of the sides would be 11.
11 * 11 = 121
Hope this helps!

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2 years ago

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2 years ago

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A 15-ft ladder rests against a vertical wall. If the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast,

3241004551 [841]

Answer:

0.44 ft/sec.

Step-by-step explanation:

Let A is the bottom of the ladder and AB is the distance from the bottom of the wall i.e. B is the bottom of the wall. If C is the top of the ladder and BC is the height of the wall.

Now, Δ ABC is a right triangle and AC is the length of the ladder i.e. hypotenuse.

Now, AC² = AB² + BC² {From Pythagoras Theorem}

Now, differentiating both sides with respect to time t, we get

$0 = 2 \times (AB) \times \frac{d(AB)}{dt} + 2 \times (BC) \times \frac{d(BC)}{dt}$

⇒ $\frac{d(AB)}{dt} = - \frac{BC}{AB} \times \frac{d(BC)}{dt}$

Now, given that $\frac{d(BC)}{dt} = - 0.33$ feet/sec.

Hence, $\frac{d(AB)}{dt} = - \frac{BC}{AB} \times (- 0.33)$ ......... (1)

Now, given that AB = 9 ft. and AC = 15 ft.

So, 15² = 9² + BC²

⇒ BC² = 144

⇒ BC = 12 feet.

Now, from equation (1), we get

$\frac{d(AB)}{dt} = - \frac{12}{9} \times (- 0.33) = 0.44$

Therefore, the bottom of the ladder is sliding away from the wall at the rate of 0.44 ft/sec. (Answer)

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2 years ago

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Step-by-step explanation:

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2 years ago

Claudia can paint a house 4 times as fast as jan can. The year they worked together it took them 8 days. How long would it take

Gwar [14]

Number of days Jan will take to complete painting work alone is 40 days and Claudia will alone take 10 days to paint complete house.

<u>Solution:</u>

Given that

Claudia can paint a house four times as fast as Jan can.

let’s assume house painted by Jan in one day = x

So house painted by Claudia in 1 day = 4x

House painted by Jan in 8 days = 8 x house painted by Jan in 1 day = 8x

House painted by Claudia in 8 days = 8 x house painted by Claudia in 1 day = 8 $\times$ 4x = 32x

As painting is completed in 8 days , so complete work of painting = House painted by Jan in 8 days + House painted by Claudia in 8 days = 8x + 32x = 40x

So 40x represent complete work of painting house.

Work of painting done by Jan in 1 day = x

if Jan alone do the work, number of days required by Jan $=\frac{\text { Complete work }}{\text { work Jan can do in one day }}$

$=\frac{40 x}{x}=40 d a y s$

Work of painting done by Claudia in 1 day = 4x

If Claudia alone do the work, number of days required by Claudia $=\frac{\text { Complete work }}{\text { work Claudia can do in one day }}$

$=\frac{40 x}{4 x}=10 d a y s$

Hence number of days Jan will take to complete painting work alone is 40 days and Claudia will alone take 10 days to paint complete house.

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2 years ago