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3 years ago

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You are having a pizza-making party. You will need 6 ounces of dough and 4 ounces of sauce for each person at the party (includi

ng yourself, the host). Once you have a total count of guests, you buy exactly the needed amount of all the ingredients. The dough and sauce that you buy weigh 130 ounces all together.How many ounces of dough did you buy?

2 answers:

Lesechka [4]3 years ago

5 0

Answer:

No. of ounces of dough= 6

No of ounces of sauce= 4

Total no. of ounces of dough= (if it is addition) 6+4= 10

(subtraction) 6-4= 2

(multiplication) 6x4= 24

(division) 6÷4=1.5

Step-by-step explanation:

olga_2 [115]3 years ago

5 0

Answer:

no

Step-by-step explanation:

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3 years ago

two similar triangles, the perimeter of the first is 74cm. and the side lengths of the other are 4.5cm, 6cm and 8cm find the len

Amiraneli [1.4K]

$\huge\mathfrak{\underline{Answer:}}$

❒ The length of longest side of first Trianlge :

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ $\large\bf{32\:cm}$

__________________________________________

$\large\bf{\underline{given:}}$

Two similar triangles
Perimeter of first Trianlge is 74 cm
Side length of second triangle are 4.5cm , 6cm and 8cm

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\bf A$}\put(0.5,-0.3){$\bf C$}\put(5.2,-0.3){$\bf B$}\end{picture}$

$\setlength{\unitlength}{0.75 cm}\begin{picture}(0,1)\thicklines\qbezier(1, 0)(1,0)(3,3)\qbezier(5,0)(5,0)(3,3)\qbezier(5,0)(1,0)(1,0)\put(2.85,3.2){$\bf P$}\put(0.5,-0.3){$\bf R$}\put(5.2,-0.3){$\bf Q$}\end{picture}$

__________________________________________

$\large\bf{\underline{To \:find :}}$

The length of longest side of first Trianlge

__________________________________________

$\large\bf{\underline{Perimeter\:of\: second\: triangle:}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{=sum\:of\:all\:sides}$

‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{=4.5+6+8}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{=18.5}$

❒ The ratio between the perimeter of two triangles :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{=\frac{perimeter\:of\:1st\: triangle}{perimeter\:of\:2nd\: triangle}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{=\frac{74}{18.5}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{=4:1}$

❒ The two triangles are similar , therefore the ratio of their sides will also be similar , i.e 4:1

➽ Let the sides of first Trianlge be x , y and z

$\large\bf{\underline{Therefore:}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹\frac{x}{4.5}=\frac{4}{1}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹\frac{y}{6}=\frac{4}{1}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹\frac{z}{8}=\frac{4}{1}}$

$\large\bf{\underline{Hence:}}$

❒ Length of first side :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹\frac{x}{4.5}=\frac{4}{1}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹x=4\times 4.5}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹x=18}$

❒ Length of second side :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹\frac{y}{6}=\frac{4}{1}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹y=4\times 6}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹y=24}$

❒ Length of third side :

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹\frac{z}{8}=\frac{4}{1}}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹z=4\times 8}$

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ $\large\bf{⟹z=32}$

__________________________________________

$\large\mathfrak{Length\:of\: largest\:side:}$

$\huge\bf{=32cm}$

5 0

2 years ago

Determine if the triangles are congruent or not?

mart [117]

Answer:

they are congruent

Step-by-step explanation:

both have the same size and angles, one is just translated

4 0

3 years ago