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3 years ago

I need help with this question about similar triangles

Mathematics

1 answer:

Colt1911 [192]3 years ago

6 0

Answer:

ST = 12 units

Step-by-step explanation:

Δ RAS and Δ TES are similar triangles, thus the ratios of corresponding sides are equal, that is, noting that SR = 21 - ST, thus

$\frac{ST}{SR}$ = $\frac{TE}{AR}$ substitute values

$\frac{ST}{21-ST}$ = $\frac{8}{6}$ ( cross- multiply )

6ST = 8(21 - ST)

6ST = 168 - 8ST ( add 8ST to both sides )

14ST = 168 ( divide both sides by 14 )

ST = 12

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2 years ago

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2 years ago

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A closed box with a square base is to have a volume of 13 comma 500 cm cubed. The material for the top and bottom of the box cos

andrezito [222]

Answer:

x = 1,5 cm

h = 6 cm

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Step-by-step explanation:

Volume of the box is :

V(b) = 13,5 cm³

Aea of the top is equal to area of the base,

Let call " x " side of the base then as it is square area is A₁ = x²

Sides areas are 4 each one equal to x * h (where h is the high of the box)

And volume of the box is 13,5 cm³ = x²*h

Then h = 13,5/x²

Side area is : A₂ = x* 13,5/x²

A(b) = A₁ + A₂

Total area of the box as functon of x is:

A(x) = 2*x² + 4* 13,5 / x

And finally cost of the box is

C(x) = 10*2*x² + 2.50*4*13.5/x

C(x) = 20*x² + 135/x

Taking derivatives on both sides of the equation:

C´(x) = 40*x - 135*/x²

C´(x) = 0 ⇒ 40*x - 135*/x² = 0 ⇒ 40*x³ = 135

x³ = 3.375

x = 1,5 cm

And h = 13,5/x² ⇒ h = 13,5/ (1,5)²

h = 6 cm

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C(min) = 135 $

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3 years ago