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3 years ago

The two triangles are similar. Find the unknown variables.

Mathematics

1 answer:

iogann1982 [59]3 years ago

7 0

Answer:

i thought it is 18 since 4 x3 =12 then 6x3 =18 I am not sure 100%

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A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

2 years ago

Question 27 twice a number x added to another number y gives 35 how ??

kenny6666 [7]

Answer:

y+2x=35

so how to get that answer if you divided 35/2= 17.5 so 17 *2= 34 +y= 35

y =1

round it down one number so y can equal 1 then you get 35

5 0

2 years ago

If b/a=2/5, what is the value of 2 (a/b)

Nina [5.8K]

$\dfrac{b}{a}=\dfrac{2}{5}\to\dfrac{a}{b}=\dfrac{5}{2}\ \ \ |\cdot2\\\\2\left(\dfrac{a}{b}\right)=2\cdot\dfrac{5}{2}\\\\2\left(\dfrac{a}{b}\right)=5$

Answer: 2(a/b) = 5

3 0

3 years ago

A ÷ (2 + 1.5) for a = 14 dont spam links and this is 6th grade work

IRINA_888 [86]

Answer:

Step-by-step explanation:

2+1.5=3.5

49/3.5=14

4 0

2 years ago

Read 2 more answers

Mai drove 260 miles using 12 gallons of gas. At this rate, how many gallons of gas would she need to drive 286 miles

Paraphin [41]

Find the unit rate which is 260/12 which is 21 and 2/3 now divide 286 by 21 and 2/3.

7 0

3 years ago