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Mice21 [21]
3 years ago
13

the length of a rectangle is 3m more than twice the width, and the area is 180m². find the dimensions of the rectangle​

Mathematics
1 answer:
Fofino [41]3 years ago
4 0

The breadth (width) of a rectangle, w, is 3m less than its length, l. If the area, A, is 180m square, what is the dimension of the rectangle?

Given:

A = 180 m^2

w = l - 3 m

Find:

l

We have one unknown in this scenario, representing length, l. So, we only need to write one equation for a numerical solution.

Since we know how the area, A, of a rectangle is related to its length, l, and breadth (width), w, we can write the equation as follows:

A = lw

Substituting our given values into the equation:

180 = l x (l - 3)

180 = l^2 - 3l

0 = l^2 - 3l - 180

This is a simple quadratic equation. We can solve it by brute force using the Quadratic Formula which states:

The roots of an equation in the for Ax^2 + Bx + C = 0 are

(-B + or minus SQRT[B^2 - 4AC])/2A

But, if we are on a timed test, there is an easier way to get to this answer rapidly.

We know the length and breadth (width) are probably integers, and that they lie three spaces apart on the number line, l = w + 3. We also know the area, A = 180, so 180 = lw. Since the SQRT[A] would equal l and w if they were the same, that’s a good first approximation.

SQRT[180] = 13.4

So, w will be less than 13.4, and l will be more.

Let’s try w = 13, and l = 13 + 3 = 16. 13 x 16 = 208 > 180 No

Let’s try w = 12, and l = 12 + 3 = 15. 12 x 15 = 180 = 180 Yes

A good test taker will be able to do this math in their head, without doing any of the calculations we’ve shown here. Let’s run through the mental steps.

180 = lw

w = l + 3

SQRT[180] = 13.4 = lw so l and w straddle 13.4

the last two digits of l and w must have a product that is a multiple of ten since 180 is a multiple of ten. 2 and 5 are three apart and a multiple of 10, so try 12 x 15 = 180 Check.The breadth (width) of a rectangle, w, is 3m less than its length, l. If the area, A, is 180m square, what is the dimension of the rectangle?

Given:

A = 180 m^2

w = l - 3 m

Find:

l

We have one unknown in this scenario, representing length, l. So, we only need to write one equation for a numerical solution.

Since we know how the area, A, of a rectangle is related to its length, l, and breadth (width), w, we can write the equation as follows:

A = lw

Substituting our given values into the equation:

180 = l x (l - 3)

180 = l^2 - 3l

0 = l^2 - 3l - 180

This is a simple quadratic equation. We can solve it by brute force using the Quadratic Formula which states:

The roots of an equation in the for Ax^2 + Bx + C = 0 are

(-B + or minus SQRT[B^2 - 4AC])/2A

But, if we are on a timed test, there is an easier way to get to this answer rapidly.

We know the length and breadth (width) are probably integers, and that they lie three spaces apart on the number line, l = w + 3. We also know the area, A = 180, so 180 = lw. Since the SQRT[A] would equal l and w if they were the same, that’s a good first approximation.

SQRT[180] = 13.4

So, w will be less than 13.4, and l will be more.

Let’s try w = 13, and l = 13 + 3 = 16. 13 x 16 = 208 > 180 No

Let’s try w = 12, and l = 12 + 3 = 15. 12 x 15 = 180 = 180 Yes

A good test taker will be able to do this math in their head, without doing any of the calculations we’ve shown here. Let’s run through the mental steps.

180 = lw

w = l + 3

SQRT[180] = 13.4 = lw so l and w straddle 13.4

the last two digits of l and w must have a product that is a multiple of ten since 180 is a multiple of ten. 2 and 5 are three apart and a multiple of 10, so try 12 x 15 = 180 Check.

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DedPeter [7]

Answer:

yes I sont now how tu understand

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3 years ago
At a sport clubhouse the coach wants to rope off a rectangular area that is adjacent to the building. He uses the length of the
Furkat [3]

Answer:

w < 8 meters ( w must be greater than 0 because length cannot be 0)

Step-by-step explanation:

One side with building is 23 meters, the other opposite side also will be 23 meters (with rope).

Let width (remaining 2 sides) be "w", he has AT MOST 39 meters of rope, so we can write:

Rope Needed = 23 + 2w < 39

Simplifying:

23 + 2w < 39\\2w < 39 - 23\\2w < 16\\w < 8

The range of possible values of w is  w meters (of course w has to be greater than 0)

5 0
3 years ago
The brand manager for a brand toothpaste must plan a campaign designed to increase brand recognition. He wants to first determin
bulgar [2K]

We need to find out how many adults must the brand manager survey in order to be 90% confident that his estimate is within five percentage points of the true population percentage.

From the given data we know that our confidence level is 90%. From Standard Normal Table we know that the critical level at 90% confidence level is 1.645. In other words, Z_{Critical}=1.645.

We also know that E=5% or E=0.05

Also, since, \hat{p} is not given, we will assume that \hat{p}=0.5. This is because, the formula that we use will have \hat{p}(1-\hat{p}) in the expression and that will be maximum only when \hat{p}=0.5. (For any other value of \hat{p}, we will get a value less than 0.25. For example if, \hat{p} is 0.4, then 1-\hat{p}=0.6 and thus, \hat{p}(1-\hat{p})=0.24.).

We will now use the formula

n=(\frac{Z_{Critical}}{E})^2\hat{p}(1-\hat{p})

We will now substitute all the data that we have and we will get

n=(\frac{1.645}{0.05})^2\times0.5(1-0.5)

n=(32.9)^2\times0.25

n=270.6025

which can approximated to n=271.

So, the brand manager needs a sample size of 271

3 0
3 years ago
-15= z/-2 answer please?​
faust18 [17]

Answer:

30

Step-by-step explanation:

-15=\frac{z}{-2}\\\\(-15)(-2)=z\\\\30=z

4 0
3 years ago
I need help ASAP please
Verdich [7]

Answer:

33

Step-by-step explanation:

first you set up the problem, supplementary angles equal 180 degrees so the equation should look like, 4x+x+15=180. then you solve from there by combining like terms and you should get x equal to 33

4 0
3 years ago
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