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3 years ago

A square of 81cm² is cut to make two rectangles, A and B

Mathematics

2 answers:

grandymaker [24]3 years ago

8 0

Answer:

Length of A: 9

Width of A: 6

Length of B: 9

Width of B: 3

Step-by-step explanation:

If you look at the diagram, you can see that the length of rectangles A and B are the same, and are also the same as they were in the original square. We can find the length of each side by finding the square root of the area of the square to give us the length and width of the square which is 9. Now that we know that the length of both rectangles A and B, we can find the width of both rectangles by taking 9, and splitting it into 3 portions of 3. Since the ratio of area is 2:1, we could also do this with the area, but since we know the lengths are the same, we know the widths are proportional to the area. Using the ratio of 2:1, and the 3 portions of 3, you can combine 2 of these portions to get 6, and since the ratio 6:3 is proportional to 2:1, these measurements can be used as the width of each rectangle. Thus, the answer given above.

katen-ka-za [31]3 years ago

8 0

Answer:

Length of A: 9

Width of A: 6

Length of B: 9

Width of B: 3

Step-by-step explanation:

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Sebastian wants to create a right triangle with side lengths 14 inches, 48 inches, and 5

allochka39001 [22]

Answer: Choice A

$\text{Yes, because } 14^2+48^2 \text{ is equal to } 50^2$

=======================================================

Explanation:

The pythagorean theorem is $a^2+b^2 = c^2$

The value of c is always the longest side, aka hypotenuse.

The order of 'a' and b doesn't matter.

So a = 14, b = 48, c = 50

We have $a^2+b^2 = 14^2+48^2 = 196+2304 = 2500$

We also have $c^2 = 50^2 = 2500$

Both sides result in 2500 which proves that $14^2+48^2 = 50^2$ is a true statement. Therefore, we do have a right triangle.

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2 years ago

If Mary has 12 more mangoes than Jason and Jason has y mangoes how many has Mary?

xeze [42]

Answer:

y+12=m

Step-by-step explanation:

m (marys mangos)

3 0

3 years ago

Two lamps marked 100 W - 110 V and 100 W - 220 V are connected i

ELEN [110]

<h2>Answer:</h2>

The power consumed in the lamp marked 100W - 110V is 15.68W

The power consumed in the lamp marked 100W - 220V is 62.73W

<h2>Step-by-step explanation:</h2>

Given:

First lamp rating

Power (P) = 100W

Voltage (V) = 110V

Second lamp rating

Power (P) = 100W

Voltage (V) = 220V

Source

Voltage = 220V

i. Get the resistance of each lamp.

Remember that power (P) of each of the lamps is given by the quotient of the square of their voltage ratings (V) and their resistances (R). i.e

P = $\frac{V^2}{R}$

Make R subject of the formula

⇒ R = $\frac{V^2}{P}$ ------------------(i)

For first lamp, let the resistance be R₁. Now substitute R = R₁, V = 110V and P = 100W into equation (i)

R₁ = $\frac{110^2}{100}$

R₁ = 121Ω

For second lamp, let the resistance be R₂. Now substitute R = R₂, V = 220V and P = 100W into equation (i)

R₂ = $\frac{220^2}{100}$

R₂ = 484Ω

ii. Get the equivalent resistance of the resistances of the lamps.

Since the lamps are connected in series, their equivalent resistance (R) is the sum of their individual resistances. i.e

R = R₁ + R₂

R = 121 + 484

R = 605Ω

iii. Get the current flowing through each of the lamps.

Since the lamps are connected in series, then the same current flows through them. This current (I) is produced by the source voltage (V = 220V) of the line and their equivalent resistance (R = 605Ω). i.e

V = IR [From Ohm's law]

I = $\frac{V}{R}$

I = $\frac{220}{605}$

I = 0.36A

iv. Get the power consumed by each lamp.

From Ohm's law, the power consumed is given by;

P = I²R

Where;

I = current flowing through the lamp

R = resistance of the lamp.

For the first lamp, power consumed is given by;

P = I²R [Where I = 0.36 and R = 121Ω]

P = (0.36)² x 121

P = 15.68W

For the second lamp, power consumed is given by;

P = I²R [Where I = 0.36 and R = 484Ω]

P = (0.36)² x 484

P = 62.73W

Therefore;

The power consumed in the lamp marked 100W - 110V is 15.68W

The power consumed in the lamp marked 100W - 220V is 62.73W

8 0

3 years ago

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Yuki888 [10]

Answer:

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Answer:

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