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3 years ago

What's the value of x

Mathematics

2 answers:

marusya05 [52]3 years ago

8 0

$25^{2} = 12.5^{2} + x^{2} 

 x^{2} = 625-156.25

 x^{2} = 468.75

x = 21.65$

Nikolay [14]3 years ago

3 0

X² = hyp² - cat²

x² = 625 - 156.25

x² = 468.75

x ≈ 21,6

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ruslelena [56]

Answer:

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

Step-by-step explanation:

Cuboid : A cuboid is a three dimension shape. The length ,breadth and height of a cuboid are not same.

A cuboid has 6 faces.
A cuboid contains 8 vertices.
A cuboid contains 12 edges .
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= 2(length×breadth+breadth×height+length×height) square units

The dimension of a cuboid is written as length×breadth×height.

The volume is( length×breadth×height) cubic units

Given that the volume of the box is 192 cubic inches.

Let x inches be the width of the cuboid.

Since the length is twice as long as its width.

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Again height is 2 inches longer than width.

Then height = (x+2) inches.

Therefore the volume of the cuboid is

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$=[2x^2(x+2)]$ cubic inches

$=(2x^3+4x^2)$ cubic inches

According to the problem,

$2x^3+4x^2=192$

$\Rightarrow 2x^3+4x^2-192=0$

$\Rightarrow 2(x^3+2x^2-96)=0$

$\Rightarrow (x^3+2x^2-96)=0$

$\Rightarrow x^3-4x^2+6x^2-24x+24x-96=0$

$\Rightarrow x^2(x-4) +6x(x-4)+24(x-4)=0$

$\Rightarrow (x-4)(x^2+6x+24)=0$

Therefore x=4

Since the all zeros of x²+6x+24 =0 is negative.

Therefore breadth = 4 inches

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and height = (4+2)inches = 6 inches.

Therefore the dimension of the cuboid is 8 inches×4 inches ×6 inches.

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Answer:

The correct option is 1.

Step-by-step explanation:

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$\angle O\cong\angle S=54.4^{\circ}$

Since all corresponding angles are congruent, therefore the triangles MNO and RTS similar.

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