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3 years ago

4x - 2y = -2 6x + 3y = 27

Mathematics

1 answer:

JulijaS [17]3 years ago

6 0

Answer:

Step-by-step explanation:

4x - 2y = -2 ------------------(I)

6x + 3y = 27 ------------------(II)

Multiply (I) by 3 & multiply (II) by 2

(I)*3 12x - 6y = -6

(II)*2 <u>12x + 6y = 54</u> { Now add & y will be eliminated}

24x = 48

x = 48/24

x = 2

Plugin the value of x in equation (I)

4*2 - 2y = - 2

8 - 2y = -2 {subtract 8 from both side}

-2y = -2 - 8

-2y = -10 {Divide both sides by -2}

y = -10/-2

y = 5

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Answer:

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

Step-by-step explanation:

We are given the following dimensions of the triangular pyramid:

Side of triangular base = 6mm

Height of triangular base = 5.2mm

Base of lateral face (triangular) = 6mm

Height of lateral face (triangular) = 8mm

a) To find Area of base of pyramid:

We know that it is a triangular pyramid and the base is a equilateral triangle. $\text{Area of triangle = } \dfrac{1}{2} \times \text{Base} \times \text{Height} ..... (1)\\$

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b) To find area of one lateral surface:

Base = 6mm

Height = 8mm

Using equation (1) to find the area:

$\Rightarrow \dfrac{1}{2} \times 8 \times 6\\\Rightarrow 24\ mm^{2}$

c) To find the lateral surface area:

We know that there are 3 lateral surfaces with equal height and equal base.

Hence, their areas will also be same. So,

$\text{Lateral Surface Area = }3 \times \text{ Area of one lateral surface}\\\Rightarrow 3 \times 24 = 72 mm^{2}$

d) To find total surface area:

Total Surface area of the given triangular pyramid will be equal to <em>Lateral Surface Area + Area of base</em>

$\Rightarrow 72 + 15.6 \\\Rightarrow 87.6\ mm^{2}$

Hence,

a) Area of the base of the pyramid = $15.6\ mm^{2}$

b) Area of one lateral face = $24\ mm^{2}$

c) Lateral Surface Area = $72\ mm^{2}$

d) Total Surface Area = $87.6\ mm^{2}$

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