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vitfil [10]
2 years ago
11

Find the unknown side length. Write your answer in simplest radical form.

Mathematics
1 answer:
Eva8 [605]2 years ago
5 0

Answer: 1. x= 20 units,   2. x= 5\sqrt{3} units    3. x= 4\sqrt{2} units.

Step-by-step explanation:

In a right triangle,

Hypotenuse^2= Perpendicular^2+Base^2  (Pythagoras theorem)

1. Hypotenuse = x , Base = 16, Perpendicular = 12

\Rightarrow\ x^2 =12^2+16^2\\\\ \Rightarrow\ x^2=144+256\\\\ \Rightarrow\ x^2=400\\\\ \Rightarrow\ x=\sqrt{400}=20

2. Hypotenuse = 14 , Base = 11, Perpendicular = x

\Rightarrow\ 14^2=x^2+11^2\\\\\Rightarrow\ 196=x^2+121\\\\\Rightarrow\ x^2=196-121\\\\\Rightarrow\ x^2 = 75\\\\\Rightarrow\ x=\sqrt{75}=\sqrt{25\times3}=5\sqrt{3}

3.  Hypotenuse = 9 , Base = x, Perpendicular =7

\Rightarrow\ 9^2=x^2+7^2\\\\\Rightarrow\ 81= x^2+49\\\\\Rightarrow\ x^2=81-49\\\\\Rightarrow\ x^2=32\\\\\Rightarrow\ x=\sqrt{32}=\sqrt{16\times2}\\\\\Rightarrow\ x=4\sqrt{2}

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vfiekz [6]

Below represents the proof that the quadrilateral QRST is a parallelogram

<h3>How to prove that QRST is a parallelogram?</h3>

The coordinates are given as:

Q = (-1,-1)

R = (2,9)

S = (-4,5)

T = (-7,-5)

Calculate the length of each side using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}

So, we have:

QR = \sqrt{(-1 - 2)^2 + (-1 -9)^2} = \sqrt{109}

RS = \sqrt{(-4 - 2)^2 + (5 - 9)^2} = \sqrt{52}

ST = \sqrt{(-7 + 4)^2 + (-5 - 5)^2} = \sqrt{109}

TQ = \sqrt{(-7 + 1)^2 + (-5 + 1)^2} = \sqrt{52}

The above computations show that opposite sides are equal.

Next, we determine the slope of each side using:

m = \frac{y_2 -y_1}{x_2 -x_1}

So, we have:

QR = \frac{9 + 1}{2 + 3} = \frac{10}3

RS = \frac{5-9}{-4 - 2} = \frac{2}3

ST = \frac{5+5}{-4 + 7} = \frac{10}3

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The above computations show that opposite sides are parallel, because they have equal slope

Hence, the quadrilateral QRST is a parallelogram

Read more about parallelograms at:

brainly.com/question/3050890

#SPJ1

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2 years ago
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