2 1/4 (2.25) is your answer
Answer:
The height of the equilateral triangle is 
Step-by-step explanation:
we know that
An equilateral triangle has three congruent sides, and three congruent angles that each measure 60 degrees
To find out the height of an equilateral triangle, apply the Pythagoras Theorem in the right triangle ABD
Remember that the height of an equilateral triangle bisects the base.
see the attached figure to better understand the problem
substitute the given values
Solve for BD
simplify
`
therefore
The height of the equilateral triangle is
Two<span> trains </span>leave different<span> cities heading toward each </span>other<span> at </span>different<span> speeds. ... At the </span>same time<span>Train B, </span>traveling 60 mph<span>, leaves Eastford heading toward Westford. ... Since an equation remains true as </span>long<span> as we perform the </span>same<span> operation ... that the train's rate is 40 </span>mph<span>, which means it </span>will travel<span> 40 </span>miles<span> in </span>one<span> hour.</span>
Answer:
The ramp should be 32.9 feet longer.
Step-by-step explanation:
When the ramp is at 
to the ground, its length can be determined by applying the appropriate trigonometric function. Let the length be represented by l, so that;
Sin θ = 
Sin = 
l = 
= 
= 33.0048
l = 33.0 feet
When the angle is reduced to 
, the length of the ramp would be;
Sin θ =
Sin =
l = 
= 
= 65.9152
l = 65.9 feet
Change in length of ramp = 65.9 - 33.0
= 32.9
The ramp should be 32.9 feet longer.
You need to do this in several steps.
1) Using the given length and width of the rectangle, find its area.
2) Then using the base and height of the triangle, find its area.
3) Since the areas are equal, set the expressions equal to each other, and solve for x.
4) Using the value of x you found, find the length and width of the rectangle and find its perimeter.
1) The area of the rectangle is A = LW
Area of Rectangle = (x + 2)x = x^2 + 2x
2) The area of the triangle is A = (1/2)bh
Area of Triangle = (1/2)(24)x = 12x
3) Set the areas equal and solve for x
x^2 + 2x = 12x
x^2 - 10x = 0
x(x - 10) = 0
x = 0 or x = 10
Since a width cannot be 0, we discard x = 0, and keep x = 10.
4) The length is x + 2 = 10 + 2 = 12
The width is x = 10
The perimeter is 2(L + W) = 2(10 + 2) = 2(22) = 44
The perimeter is 44 cm.
