This is a classic example of a 45-45-90 triangle: it's a right triangle (one angle of 90) & two other sides of the same length, which means two angles of the same length (and 45 is the only number that will work). With a 45-45-90 triangle, the lengths of the legs are easy to determine:
45-45-90
1-1-sqrt2
Where the hypotenuse corresponds to sqrt2.
Now, your hypotenuse is 10.
To figure out what each leg is, divide 10/sqrt2 (because sqrt2/sqrt2 = 1, which is a leg length in the explanation above).
Problem: you can't divide by radicals. So, we'll have to rationalize the denominator:
(10•sqrt2)/(sqrt2•sqrt2)
This can be rewritten:
10sqrt2/sqrt(2•2)
=10sqrt2/sqrt4
=10sqrt2/2
=5sqrt2
Hope this helps!!
Answer:
The solution is 8x2 + 16x + 8. The region can be divided into a triangle and a rectangle.
Area of Triangle=
1
2
(2x + 2)(2x)
Area of Triangle = 2x2 + 2x
Area of Rectangle: (2x + 2)(3x + 4)
Area of Rectangle: 6x2 + 14x + 8
Sum of Two Regions: 8x2 + 16x + 8
Step-by-step explanation:
3a+b+c
The perimeter is two times one side (to account for the opposite) and two times the adjacent side. So if the sides would be x and y, the perimeter would be 2*x + 2*y.
So, knowing that the sum is 16a+8b-6c, if we subtract the given side 5a+3b-4c from this, what remains is two times the "other" side:
16a+8b-6c - 2*(5a+3b-4c) =
16a+8b-6c -10a-6b+8c =
6a+2b+2c
half of that is
(6a+2b+2c)/2 = 3a+b+c
The dimensions of the larger cuboid are 25/10 = 2.5 times those of the smaller one. {length, width} = 2.5*{4 cm, 7 cm) = {10 cm, 17.5 cm}
