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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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An arithmetic sequence has t1 = 6 and common difference 2 find t12 and s12​
Sergeeva-Olga [200]

Answer:

See below ~

Step-by-step explanation:

Finding t₁₂ :

⇒ t₁₂ = t₁ + 11d

⇒ t₁₂ = 6 + 11(2)

⇒ t₁₂ = 6 + 22

⇒ t₁₂ = 28

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

Finding S₁₂ :

⇒ S₁₂ = 12/2 × 2t₁ + (12 - 1)d

⇒ S₁₂ = 6 × 2(6) + 11(2)

⇒ S₁₂ = 6 × 12 + 22

⇒ S₁₂ = 6 × 34

⇒ S₁₂ = 204

4 0
1 year ago
how many square feet will cover a rectangle 60 feet by 20 feet? Explain how you determined your answer
nika2105 [10]

Answer:

1200

Step-by-step explanation:

2 times 6 = 12

12 times 100 = 1200

Hope this helps if does not please let me know thanks!

7 0
3 years ago
Function lis defined by the equation r
Amiraneli [1.4K]

Answer:

Both have the same y-intercept (-9)

Step-by-step explanation:

✔️Function 1, r = ⅝t - 9, is given in the slope-intercept form, y = mx + b.

b = y-intercept = -9

y-intercept for Function 1 = -9

✔️Function 2, using the table given, the y-intercept is the value of r when t = 0.

Thus, r = -9 when t = 0.

y-intercept for Function 2 = -9

✔️Both functions has the same y-intercept. None is greater than the other.

6 0
3 years ago
The equation of line q is y =
shtirl [24]
These are not the exact numbers but just plug in the numbers of yours Because we know that q is a perpendicular line to p we know that its slope is the negative reciprocal of the slope of p. So its slope is 7/10. Now we just need to find its y-intercept. To do that we write what we know about line q. So we know that the equation for line q looks like:

y = (7/10)x + b

We also know that q passes through the point (8,7), so we now plug that in and solve for b:

7 = (7/10)(8) + b
7 - (56/10) = b
(70/10) - (56/10) = b
14/10 = 7/5 = b

So now that we have solved for the y-intercept, we know that the equation for line q is:

y = (7/10)x + 7/5
3 0
3 years ago
City park is a right triangle with a base of 49 yrds and a height of 25 yard in a map The park is a basic 3 inches and the heigh
ASHA 777 [7]

Answer:

3/49

Step-by-step explanation:

The area of a rectangle is found using A = l*w. At the park, it measures A = 49*25 = 1,225 yards².

On the map the area is A = 3*25 = 75 inches².

The ratio of the area of the map to the area of the park is found by placing 75 ovre 1,225. Then simplify if possible.

\frac{75}{1225} = \frac{3*25}{49*25} = \frac{3}{49}

7 0
3 years ago
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