I want you to imagine as you read this or you can draw through the help of my explanation and see yourself:
1↪Draw triangle ABC where BC>AC
2↪D is any point on AC such that CD=CB
3↪Roughly drawing , you can assume CD=CB and and join BD
4↪SO triangle ABC which is a big triangle is divided into Triangles ABD and BDC
5↪See in triangle BDC ,CD=CB so, base angles of isosceles triangle are equal:
<CDB=<CBD = x (assume) which means x is acute angle since CDB and CBD are are in same triangle with same measure and there can't be any two obtuse angle in any traingle. So x must be acute.
6↪Now see in traingle ABD,
<ADB=180-<CDB=180-x=obtuse angle
...check yourself ...just subtract any acute angle from 180 you will get only obtuse angle (ie angle greater than 90)
That means in triangle ABD , one angle ADB is obtuse which means remaining <ABD and < BAD are acute. [PROVED]
❇Main Concept Used Here:
↪In any triangle there can be maximum of one obtuse angle...so remaining two must be acute angle otherwise interior angles sum can't be equal to 180.
A=w*L
Frame A=16*22
Portrait A=12*18
Subtract 352 from 216
The area of the frame is 136in^2.
Answer:
82 inches
Step-by-step explanation:
The difference between consecutive even integers is 2, thus
let the legs be n and n + 2
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
n² + (n + 2)² = 58² ← expand and simplify left side
n² + n² + 4n + 4 = 3364 ( subtract 3364 from both sides )
2n² + 4n - 3360 = 0 ( divide all terms by 2 )
n² + 2n - 1680 = 0 ← in standard form
(n + 42)(n - 40) = 0 ← in factored form
Equate each factor to zero and solve for n
n + 42 = 0 ⇒ n = - 42
n - 40 = 0 ⇒ n = 40
But n > 0 ⇒ n = 40
and n + 2 = 40 + 2 = 42
Thus sum of legs = 40 + 42 = 82 inches
2100|2
1050|2
525|3
175|5
35|5
7|7
1|
2100 = 2 × 2 × 3 × 5 × 5 × 7 = 2² × 3 × 5² × 7
Answer:
Removing the perfect square 4 in 12 we get 2√3
Step-by-step explanation:
The square root of 12 is
√12 = √(4 x 3)
√12 = 2√3.
There's no special trick here, but it's usually easy to check whether a small number is divisible by 4. Keep this in mind when looking for factors.
Removing the perfect square 4 in the square root of 12 we get 2√3.
Here 4 is a perfect square it can be written as
√4 =√2^2
√4 =2
