How to work out the length and the width of the rectangle

Mathematics

1 answer:

wariber [46]3 years ago

3 0

Rectangle:

Define x:

Let the width be x.
width = x
Length = 3x + 4

Find Area:

Area = x(3x + 4)

Square:
Length of square = Length of rectangle = 3x + 4

Area = (3x + 4)²

Area of square is 66cm² more than area of rectangle.
⇒ (3x+ 4)² = x(3x + 4) + 66

Solve x;
(3x+ 4)² = x(3x + 4) + 66

Remove brackets:
9x² + 24x + 16 = 3x² + 4x + 66

Take away 3x² + 4x + 66 from both sides:
6x² + 20x - 50 = 0

Divide by 2:
3x² + 10x - 25 = 0

Factorise:
<span>(3x - 5)(x + 5) = 0

Apply product multiplication property
</span>(3x - 5)= 0 or (x + 5) = 0
x = 5/3 or x = -5 (rejected, since x cannot be negative)

Width x= 5/3 cm
Length = 3x + 4 = 3(5/3) + 4 = 9 cm

Answer: The width is 5/3 cm and length is 9 cm.

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A sphere has a surface area of 36π ft2. Find the volume of the sphere.

Stella [2.4K]

The surface area of the sphere is given by the equation

$A=4\pi * r^{2}$ ,

where A is the surface area and r is the radius.

We want to find the volume of the sphere, which is given by the equation

$V = \frac{4}{3} * \pi * r^{3}$ ,

where V is the volume and r is the radius.

Looking at these equations, we see that they both involve the sphere's radius. If we know what r is, we can calculate the volume.

We know that the sphere's surface area is $36 \pi$ . Plugging that in for A in the surface area equation, we get

$36 \pi=4\pi * r^{2}$ , then divide by $\pi$

$36 = 4 * r^{2}$ , then divide by 4

$r^{2} = 9$ , then take the square root of both sides

$r = 3$

So the radius of the sphere is 3. Plugging this into the volume equation,

$V = \frac{4}{3} * \pi * 3^{3}$ , simplify terms

$V = \frac{4}{3} * \pi * 27$ , multiply $\frac{4}{3}$ by 27

$V = 36 * \pi$

So the volume of the sphere is $36\pi$ .

6 0

4 years ago

Read 2 more answers

Surface area of a cone. Can someone please explain?

Vlad1618 [11]

Answer:

H. 163.3

Step-by-step explanation:

The formula for the surface area of a cone is πrl(area of the side) + π $r^{2}$ (area of the base), where l is the slant height and r is the radius. We know that the radius is 4 and the slant height is 9, so we plug it into the equation to get π(4)(9) + $\pi r^{2}$ = 36π+16π = 52π which rounds to 163.3.