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3 years ago

What is the correct answer for this

Mathematics

1 answer:

arlik [135]3 years ago

8 0

The measure of length a is 21

Step-by-step explanation:

ΔABC ~ ΔDBE

I use equation :

$\ \: \: \: \: \: \: \: \: \: \: \: \: \frac{ab}{bd} = \frac{bc}{be} \\ \: \: \: \frac{36 + 18}{18} = \frac{a + 42}{a} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \frac{54}{18} = \frac{a + 42}{a} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3 = \frac{a+42}{a}\\ \: \: \: \: \: \: \: \: \: \: \: \: \: 3a = a + 42 \\ \: \: \: \: \: \: 3a - a = 42 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2a = 42 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a = \frac{42}{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: a = 21$

So, the measure of length a is 21

Hope it helpful and useful :)

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Part A

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Answer:

Part A) The area of triangle i is $3\ cm^{2}$

Part B) The total area of triangles i and ii is $6\ cm^{2}$

Part C) The area of rectangle i is $20\ cm^{2}$

Part D) The area of rectangle ii is $32\ cm^{2}$

Part E) The total area of rectangles i and iii is $40\ cm^{2}$

Part F) The total area of all the rectangles is $72\ cm^{2}$

Part G) To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) The surface area of the prism is $78\ cm^{2}$

Part I) The statement is false

Part J) The statement is true

Step-by-step explanation:

Part A) What is the area of triangle i?

we know that

The area of a triangle is equal to

$A=\frac{1}{2} (b)(h)$

we have

$b=4\ cm$

$h=1.5\ cm$

substitute

$A=\frac{1}{2} (4)(1.5)$

$Ai=3\ cm^{2}$

Part B) Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii?

we know that

If Triangles i and ii are congruent

then

Their areas are equal

$Aii=Ai$

The area of triangle ii is equal to

$Aii=3\ cm^{2}$

The total area of triangles i and ii is equal to

$A=Ai+Aii$

substitute the values

$A=3+3=6\ cm^{2}$

Part C) What is the area of rectangle i?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=2.5\ cm$

$h=8\ cm$

substitute

$Ai=(2.5)(8)$

$Ai=20\ cm^{2}$

Part D) What is the area of rectangle ii?

we know that

The area of a rectangle is equal to

$A=(b)(h)$

we have

$b=4\ cm$

$h=8\ cm$

substitute

$Aii=(4)(8)$

$Aii=32\ cm^{2}$

Part E) Rectangles i and iii have the same size and shape. What is the total area of rectangles i and iii?

we know that

Rectangles i and iii are congruent (have the same size and shape)

If rectangles i and iii are congruent

then

Their areas are equal

$Aiii=Ai$

The area of rectangle iii is equal to

$Aiii=20\ cm^{2}$

The total area of rectangles i and iii is equal to

$A=Ai+Aiii$

substitute the values

$A=20+20=40\ cm^{2}$

Part F) What is the total area of all the rectangles?

we know that

The total area of all the rectangles is

$At=Ai+Aii+Aiii$

substitute the values

$At=20+32+20=72\ cm^{2}$

Part G) What areas do you need to know to find the surface area of the prism?

To find the surface area of the prism, we need to know only the area of triangle i and the area of rectangle i and the area of rectangle ii, because the area of triangle ii is equal to the area of triangle i and the area of rectangle iii is equal to the area of rectangle i

Part H) What is the surface area of the prism? Show your calculation

we know that

The surface area of the prism is equal to the area of all the faces of the prism

The surface area of the prism is two times the area of triangle i plus two times the area of rectangle i plus the area of rectangle ii

$SA=2(3)+2(20)+32=78\ cm^{2}$

Part I) Read this statement: “If you multiply the area of one rectangle in the figure by 3, you’ll get the total area of the rectangles.” Is this statement true or false? Why?

The statement is false

Because, the three rectangles are not congruent

The total area of the rectangles is $72\ cm^{2}$ and if you multiply the area of one rectangle by 3 you will get $20*3=60\ cm^{2}$

$72\ cm^{2}\neq 60\ cm^{2}$

Part J) Read this statement: “If you multiply the area of one triangle in the figure by 2, you’ll get the total area of the triangles.” Is this statement true or false? Why?

The statement is true

Because, the triangles are congruent

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