<span>80 ft^2
Looking at the figure, you can easily determine that it's made of two separate figures, a rectangle that's 2 feet by 16 feet, and a triangle that has sides of 16 feet, 10 feet, and 10 feet. The triangle can then be divided into two right triangles with a hypotenuse of 10 feet and one leg of 8 feet, so you can use the Pythagorean theorem to calculate the other leg (which is also the height of the large triangle mentioned above). That value is sqrt(10^2 - 8^2) = sqrt(100 - 64) = sqrt(36) = 6.
So we now know that the large 16,10,10 triangle has a base of 16 and a height of 6. So let's calculate the area of the entire figure.
A = 2*16 + 16*6/2
A = 32 + 16*3
A = 32 + 48
A = 80
So the area of the entire figure is 80 square feet.</span>
An equilateral triangles has 3 equal sides and 3 equal angles.
All the angles of an equilateral triangle have a measure of 60 degrees.
Using the Pythagorean theorem, the length of the hypotenuse squared is the length of one leg squared plus the length of another leg squared.
Here's the equation for the Pythagorean theorem.
Let c be the length of the hypotenuse.
Let a and b be the length of the two legs.
a^2 + b^2 = c^2
Have an awesome day! :)
Answer: Elizabeth and Manuel have a distance of 4 meters between them.
Step-by-step explanation: Please refer to the picture attached.
From the information given, Elizabeth is directly behind Hannah and directly left of Manuel. That means we have three points which are HEM, that is, we now have triangle HEM. The longest side (hypotenuse) which is the distance between Hannah and Manuel is given as 5 meters while the other side the distance between Hannah and Elizabeth is given as 3 meters.
We shall apply the pythagoras theorem in solving for the unknown side, EM.
The Pythagoras theorem states thus;
AC² = AB² + BC²
Where AC is the hypotenuse, and AB and BC are the other two sides.
Substituting for the known values, we now have;
5² = 3² + EM²
25 = 9 + EM²
Subtract 9 from both sides of the equation
16 = EM²
Add the square root sign to both sides of the equation
√16 = √EM²
4 = EM
Therefore the distance between Elizabeth and Manuel is 4 meters
Answer:
You cant simplify it??????
Step-by-step explanation:
Here,
let width(b)be x then,
length (l)=9cm+x
area =112 sq cm
now,
area of rectangle=l*b
or, 112=(9+x)x
or, 112=9x+x^2
or, 0=x^2+9x-112
or, 0=x^2+(16-7)x-112
or, 0=x^2+16x-7x-112
or, 0=x(x+16)-7(x+16)
or, 0=(x-7)(x+16)
either,
0=x-7
or,7=x
x=7cm
Or,
0=x+16
or, -16=x
x= -16[impossible,as distance is never negative] so,
x=7cm
therefore,length = 7cm + 9 cm = 16cm and width = 7cm.
;)
