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Kamila [148]
3 years ago
8

Find the missing side lengths and leave your answers as radicals in the simplest form.

Mathematics
2 answers:
Readme [11.4K]3 years ago
7 0

Answer:

a = 4

b = 2√2

Step-by-step explanation:

First, we will calculate the sine of 45°, which is equal to the length of the opposite side (2√2) divided by the length of the hypotenuse (a).

sin 45° = 2√2 / a

a = 2√2 / sin 45°

We know than sin 45° = √2/2

a = (2√2) / (√2/2) = 4

Then, we calculate the tangent of 45°, which is equal to the length of the opposite side (2√2) divided by the length of the adjacent side (b).

tan 45° = 2√2 / b

b = 2√2 / tan 45°

We know that tan 45° = 1

b = 2√2 /  1 = 2√2

goblinko [34]3 years ago
3 0
Right triangle 45 45 90
so b = 2√2

and
a^2 = (2√2)^2 +  (2√2)^2
a^2 = 8 + 8 
a^2 = 16
a = 4
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3 years ago
A square piece of paper has an area of x2 square units. A
Dmitry_Shevchenko [17]

Answer:

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

Step-by-step explanation:

Area of square x^2

area of rectangle is given by length * width

Length of rectangular strip = x

width of rectangular strip = 2

area of rectangular strip =  length * width = 2*x = 2x

Area of square piece of paper when  rectangular strip is taken away from it

= Area of square - area of rectangular strip

= x^2 -2x

It is given that Area of square piece of paper when  rectangular strip is taken away from it is 120 square units.

Thus,

x^2 -2x = 120\\=> x^2 -2x -120 = 0\\=> x^2 -12x +10x-120\\=> x(x-12) +10(x-12)\\=> (x+10)(x-12) = 0\\\\

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either x+10 = 0 or x -12= 0

x = -10 or x = 12

but length cannot  be negative hence neglecting x = -10

hence value of x is 12.

Hence,

Length of rectangular strip = 12

area of rectangular strip =   2*12 = 24

Area of square =  x^2 = 12^2 = 144

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