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faust18 [17]
3 years ago
7

The length of a rectangle is 3cm more than twice the width. The perimeter is 84 cm. Find the dimensions .

Mathematics
1 answer:
blsea [12.9K]3 years ago
4 0

Width of the rectangle is 13 cm and length is 29 cm.

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

Step 1:

Given perimeter of the rectangle = 84 cm. Let the width be x, then the length of the rectangle = 2x + 3. Use the formula for perimeter of a rectangle = 2(length + width) to find the dimensions.

84 = 2(2x + 3 + x) = 2(3x + 3) = 6(x + 1) [taking 3 as common factor outside)

⇒ 84 = 6x + 6

⇒ 78 = 6x

∴ x = 13

⇒ Width of the rectangle = 13 cm

∴ Length of the rectangle = 2x + 3 = 29 cm

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agasfer [191]

Answer:

Step-by-step explanation:

Area of square = area of triangle

side*side = \dfrac{1}{2}b*h\\\\\\x*x=\dfrac{1}{2}*(x+1)(x+2)\\x^{2}=\dfrac{1}{2}[x*x +x*2+1*x+1*2]\\\\\\x^{2}=\dfrac{1}{2}[x^{2}+2x+x+2]\\\\\\x^{2}=\dfrac{1}{2}[x^{2}+3x+2]\\\\\\Multiply \ both \ sides \ by \ 2\\\\2x^{2}=x^{2}+3x+2\\\\2x^{2}-x^{2}-3x-2 = 0

x² - 3x - 2 = 0

8 0
3 years ago
P, Q, V, and K are collinear with V between K and P, and Q between V and K. If VP = 14x + 4, PK = x + 630, VQ = 17x + 6, and KQ
Ierofanga [76]

It's given in the question,

P, Q, V and K are collinear.

VP = 14x + 4

PK = x + 630

VQ = 17x + 6

KQ = 11x + 5

By segment addition postulate,

KQ + VQ + VP = KP

Substitute the values in the expression,

(11x + 5) + (17x + 6) + (14x + 4) = x + 630

(11x + 17x + 14x) + (5 + 6 + 4) = x + 630

42x + 15 = x + 630

42x - x = 630 - 15

41x = 615

x = \frac{615}{41}

x = 15

Therefore, value of VP = (14x + 4)

                                      = 14(15) + 4

                                      = 214 units

Learn more,

brainly.com/question/628239

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3 years ago
The area of the city of Vancouver is 115 km^2. if the shape of Vancouver is approximately a square, how wide is the city of Vanc
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Answer:

The wide of the city is 10.7km

Step-by-step explanation:

To solve this we first have to know the formula to calculate the area of ​​a square

a = area = 115 km²

s = side

a = s * s

now we replace with the known values

115 km² = s * s

115 km² = s²

√(115 km²) = s

10.724km = s

Round to the nearest tenth

s = 10.724km = 10.7km

The wide of the city is 10.7km

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The total surface area of a cube is 96cm2, find its volume.
Setler [38]

Answer:

\huge\boxed{V=64cm^3}

Step-by-step explanation:

The formula of a surface area of a cube:

SA=6a^2

The formula of a volume of a cube:

V=a^3

We have

SA=96cm^2

Calculate the edge length (<em>a</em>).

6a^2=96           <em>divide both sides by 6</em>

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Calculate the volume of a cube:

V=4^3=64(cm^3)

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