What is the greatest common factor of 14 and 37?

Aryan wants to plant a flower on the ground in the form of a rhombus. The diagonals of the rhombus measures 42 cm and 56 cm. Fin

Vlad1618 [11]

Given info:-

Aryan wants to plant a flower on the ground in the form of a rhombus.The diagonals of the rhombus measures 42 cm and 56 cm.

Find the perimeter of the field ?

Explanation:-

Given that

rhombus.The diagonals of the rhombus measures 42 cm and 56 cm.

Let consider a rhombus ABCD

Let AC = (d1) = 42 cm

Let BD = (d2) = 56 cm

We know that

The digonals of a rhombus bisects each other at 90°.

AC = AO+OC

⇛ AC = 2 AO = 2 OC

⇛ AO = OC = AC/2

⇛ AO = OC = 42/2 = 21 cm

and

BD = BO+OD

⇛ BD = 2 BO = 2 OD

⇛ BO = OD = BD/2

⇛ BO = OD = 56/2 = 28 cm

We have,

∆AOB is a right angled triangle

By Pythagoras theorem,

AB² = AO²+OB²

⇛ AB² = 21²+28²

⇛ AB² = 441+784

⇛ AB² = 1225

⇛ AB = ±√1225

⇛ AB = ±35

AB is the length of the side which cannot be negative.

AB = 35 cm

We know that

All sides are equal in a rhombus

⇛ AB = BC = CD = DA

As we know

The Perimeter of a rhombus = 4×Side units

The perimeter of the rhombus ABCD

⇛ 4AB = 4BC = 4CD = 4DA

⇛ 4×35 cm

⇛ Perimeter = 140 cm

∴ The perimeter of the given field is 140 cm.

6 0

3 years ago

What is the volume of this rectangular prism

qaws [65]

Volume is 5cm^3 teehee

8 0

3 years ago

Read 2 more answers

Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tent

nalin [4]

Answer:

The last one $(x=11.3, y=8)$ .

Step-by-step explanation:

1) There are three trigonometric ratios for right-angled triangles.

$sin()=\frac{opposite}{hypotenuse}\\cos()=\frac{adjacent}{hypotenuse}\\tan()=\frac{opposite}{adjacent}$

In a right triangle, the hypotenuse, h, is the side opposite the right angle. Relative to the acute angle θ, check the attachment, the legs are called the opposite side, o, and the adjacent side a.

2) In this case, we are given a length and an angle to find x and y.

Let's find x first. To find x we need to use $sin()=\frac{opposite}{hypotenuse}$ .

$sin(45)=\frac{8}{x}\\sin(45)x=8\\x=\frac{8}{sin(45)} \\x=11.31$

Find y.

Notice that, we can use the Pythagorean Theorem $(c^2=a^2+b^2)$ to find y.

$c^2=a^2+b^2$

$11.31^2=8^2+b^2\\11.31^2 - 8^2 = b^2\\63.9161 = b^2\\\sqrt{63.9161} = b\\b = 7.99$

3) Round them off to the nearest tenth.

$x=11.31\\x=11.3$

$y=7.99\\y=8$

Therefore, the correct choice is the last one $(x=11.3, y=8)$ .

4 0

2 years ago

Solve each system of equations (systems with 3 variables)

Natasha2012 [34]

Answer:

x = 2 , y = 5 , z = -1 You are correct!!!

Step-by-step explanation:

Solve the following system: