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3 years ago

This is a square pyramid. What is the length of the base? h=3 v=36

Mathematics

1 answer:

Ulleksa [173]3 years ago

7 0

volume of square pyramid = S^2*h/3

volume = 36

h = 3

36 = S^2 *3/3

36 = S^2

S = sqrt(36)

S = 6

length of base = 6

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3 years ago

A triangle has base 2x+1 and height 6x-3. What value of x would give an area of 240m2?

GREYUIT [131]

Answer:

The values of x which would give an area of 240m² would be:

$x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}$

Step-by-step explanation:

Given

The base of triangle b = 2x+1

The height of triangle h = 6x-3

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The Area of the triangle has the formula

A = 1/2 × b × h

substituting b = 2x+1, h = 6x-3 and A = 240

$240\:=\:\frac{1}{2}\:\left(2x+1\right)\:\times \left(6x-3\right)$

$480=\left(2x+1\right)\left(6x-3\right)$

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Subtract 480 from both sides

$12x^2-3-480=480-480$

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$3\left(2x+\sqrt{161}\right)\left(2x-\sqrt{161}\right)=0$

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

$2x+\sqrt{161}=0\quad \mathrm{or}\quad \:2x-\sqrt{161}=0$

solving

$2x+\sqrt{161}=0$

$2x=-\sqrt{161}$

Divide both sides by 2

$\frac{2x}{2}=\frac{-\sqrt{161}}{2}$

$x=-\frac{\sqrt{161}}{2}$

also solving

$2x-\sqrt{161}=0$

$2x=\sqrt{161}$

Divide both sides by 2

$\frac{2x}{2}=\frac{\sqrt{161}}{2}$

$x=\frac{\sqrt{161}}{2}$

Therefore, the values of x which would give an area of 240m² would be:

$x=-\frac{\sqrt{161}}{2},\:x=\frac{\sqrt{161}}{2}$

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3 years ago

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vova2212 [387]

Answer:

Step-by-step explanation:

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3 years ago