The lengths of the other two sides of the right triangle are 12 and 13
<h3>Pythagorean theorem </h3>
From the question, we are to determine the lengths of the other sides of the triangle
From the given information,
The other sides have lengths that are consecutive integers
Thus,
If the length of the other side is x
Then,
The hypotenuse will be x + 1
By the <em>Pythagorean theorem</em>, we can write that
(x+1)² = x² + 5²
(x+1)(x+1) = x² + 25
x² + x + x + 1 = x² + 25
x² - x² + x + x = 25 - 1
2x = 24
x = 24/2
x = 12
∴ The other leg of the right triangle is 12
Hypotenuse = x + 1 = 12 + 1 = 13
Hence, the lengths of the other two sides are 12 and 13
Learn more on Pythagorean theorem here: brainly.com/question/4584452
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Answer:
∠RPQ = 27
Step-by-step explanation:
In ΔSRQ,
∠R = 90
∠SQR = 36°
∠R + ∠SQR + ∠RSQ = 180 {Angle sum property of triangle}
90 + 36 + ∠RSQ = 180
126 + ∠RSQ = 180
∠RSQ = 180 - 126
∠RSQ = 54°
∠PSQ +∠RSQ = 180 {Linear pair}
∠PSQ + 54 = 180
∠PSQ = 180 - 54
∠PSQ = 126
In ΔPSQ,
SQ = PS ,
So, ∠SQP = ∠SPQ {Angles opposite to equal sides are equal}
∠SQP = ∠SPQ =x
∠PSQ + x +x = 180 {Angle sum property of triangle}
126 + 2x = 180
2x = 180 - 126
2x = 54
x = 54/2
x = 27
∠RPQ = 27°
Answer:
Step-by-step explanation:
(x²-6x)+(y²+8y)=-21
(x²-6x+9)+(y²+8y+16)=-21+9+16
(x-3)²+(y+4)²=4
center=(3,-4),radius=√4=2
The formula for an area of a circle is
A=pi times radius squared
there for you do pi times 9.5 to the power of two/squared (radius is half of the diameter so 19 divided by 2 is 9.5)
pi times 9.5 squared
= 283.5
I rounded to the nearest tenths
