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irina [24]
3 years ago
13

The length of a rectangle is four times its width. Its perimeter is no greater than 170 cm. Find the greatest possible dimension

s of the rectangle.
Mathematics
1 answer:
juin [17]3 years ago
7 0

Step-by-step explanation:

let the length be =L

the width is 4 × the length

so the width will be 4L

the formular for the perimeter of a rectangle is =2(L +W)

170=2(L +4L)

170=2(5L)

170=10L

17=L

so the width is 4 × the length

17×4

=68

L=17

W=68

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Triangle ABC has perimeter 22cm
ASHA 777 [7]

9514 1404 393

Answer:

  not a right triangle

Step-by-step explanation:

The perimeter is 22, so we have ...

  AB +BC +CA = 22

  8 + 5 + CA = 22

  CA = 22 -13 = 9

If this is a right triangle, the sum of the squares of the short sides will be equal to the square of the long side.

  AB² +BC² = 8² +5² = 64 +25 = 89

This is not the same as ...

  CA² = 9² = 81

The triangle is not a right triangle.

_____

<em>Additional comment</em>

If you're familiar with a few Pythagorean triples, you know that a couple involving a side length 5 are (3, 4, 5) and (5, 12, 13). That is, (5, 8, 9) is NOT a Pythagorean triple, so you know immediately that those side lengths do not form a right triangle. (No calculation is necessary.)

6 0
3 years ago
Whats the mean of 72+72+72+79+82+82+88?
creativ13 [48]

Answer:

78.1428571429

Step-by-step explanation:

6 0
3 years ago
What are the endpoint coordinates for the mid segment of △PQR that is parallel to PQ?
diamong [38]

Answer:

So the end points of the mid segment are:

S(-3.5,0.5)

T(-1,-0.5)

Step-by-step explanation:

First of all we need to list the co-ordinates of the points of the triangle shown.

P\rightarrow(-3,3)

Q\rightarrow(2,1)

R\rightarrow(-4,-2)

We need to find mid segment of the triangle which is parallel to segment PQ. This would mean we need to find midpoints of segment PR and QR and then join the points to get mid segment.

Midpoint Formula:

(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

Midpoint of PR:

S((\frac{-3+(-4)}{2},\frac{3+(-2)}{2})\\\\(\frac{-3-4}{2},\frac{3-2}{2})\\\\(\frac{-7}{2},\frac{1}{2} )

S(-3.5,0.5)

Midpoint of QR:

T(\frac{2+(-4)}{2},\frac{1+(-2)}{2})\\\\(\frac{2-4}{2},\frac{1-2}{2} )\\\\(\frac{-2}{2},\frac{-1}{2}

T(-1,-0.5)

So the end points of the mid segment are:

S(-3.5,0.5)

T(-1,-0.5)

By mid segment theorem we know that the line joining midpoints of two sides of a triangle is parallel to the 3rd side.

∴ We know ST is parallel to PQ  

4 0
3 years ago
Read 2 more answers
The measure of a vertex angle of an isosceles triangle is 120° and the length of a leg is 8 cm. Find the length of a diameter of
Goryan [66]

ANSWER

The length of a Diameter is 3.714

EXPLANATION

The circumscribed triangle is shown in the attachment.

We use the cosine ratio to find the altitude of the isosceles triangle.

\cos(60 \degree)  =  \frac{altitude}{hypotenuse}

\cos(60 \degree)  =  \frac{altitude}{8}

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Let the upper half of the altitude be y cm.

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y\sin(60 \degree)  = 4 - y

y\sin(60 \degree)   + y= 4

(\sin(60 \degree)   + 1)y= 4

y=  \frac{4}{\sin(60 \degree)   + 1}

y = 16 - 8 \sqrt{3}

y=1.857

The diameter is 2y

d = 32 - 16 \sqrt{3}

=2(1.875)

The length of a Diameter is 3.714

7 0
3 years ago
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At the bookstore 40 copies of a popular paperback book fit perfectly on a 5 foot shelf
stellarik [79]

Answer:

8?

Step-by-step explanation:

5x8=40

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3 years ago
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