The alloy contains 10.5 pounds of copper.
Answer:
x = ±2
Step-by-step explanation:
3x ^2 -4 = 8
Add 4 to each side
3x ^2 -4+4 = 8+4
3x^2 =12
Divide each side by 3
3x^2 =12
3x^2/3 = 12/3
x^2 = 4
Take the square root of each side
sqrt(x^2) = ±sqrt(4)
x = ±2
<u>Given</u><u> info</u><u>:</u><u>-</u>
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 ?
<u>Explanation</u><u>:</u><u>-</u>
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
<em>∴</em><em> </em><em>T</em><em>he perimeter of the given field is 140 cm.</em>
Sorry I don't have enough time to deal with this problems, I believe that by using this formula you will easily come out with your answer. In the first one that has all sides you must use the law of cosines. Here is the formulas . Keep it because it is very helpful
