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3 years ago

Can you have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23? Explain.

Mathematics

2 answers:

dezoksy [38]3 years ago

7 0

No you can't because a right angle is 90

Norma-Jean [14]3 years ago

3 0

Answer: No,it is not possible to have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23.

Step-by-step explanation:

According to the Pythagorean triplet, in a right angled triangle the hypotenuse is the longest side.

and it is given by $m^2+1$ and other two legs are given by $m^2-1$ and $2m$

Now, the longest side= $m^2+1=23$

$\Rightarrow\ m^2=23-1\\\Rightarrow\ m^2=22$

But 22 is not a perfect square

Since $4^2=16$ and $5^2=25$ , therefore the square root of 22 lies between 4 and 5.

Hence, it is not possible to have a right triangle where the lengths of the legs are whole numbers and the length of the hypotenuse is 23.

You might be interested in

a 1ft long piece of wire needs to be divided into two pieces which will form the shape of a circle and a square. Determine the l

yan [13]

Answer:

Length of wire for circle is 0.44 ft

Length of wire for square is 0.56 ft

Step-by-step explanation:

Let x is circumference of the circle

then

(1-x) = perimeter of the square

Find the radius of the circle

r = (x/2.π)

Find the area of the circle

a = π(x/2π)^2

a = π(x^2/4π^2)

Cancel π

a = x^2/4π

Find the area of the square:

a = (1-x/4)^2

a = (1-2x+x^2)/16

Total area

A = (x^2/4π)+(1-2x+x^2/16)

A = 4x^2+3.142-6.284x+3.142x^2

A = 7.142x^2-6.284x+3.142

Find the axis of symmetry [x = -b/(2a)]

x = -(-6.284)/{2.(7.142)}

x = 6.284/14.284

x = 0.44 ft, the piece of wire creating a circle

and

1 - 0.44 = 0.56 ft, the piece of wire creating the square

These lengths should give minimum area of the circle and square together

7 0

3 years ago

Which choice is equivalent to the expression below?

alekssr [168]

Answer: OPTION A

Step-by-step explanation:

We need to remember that Product of powers property, which states that:

$(a^m)(a^n)=a^{(m+n)}$

Let's check the options:

A. For $5^9*5^{\frac{9}{10}}*5^{\frac{6}{100}}*5^{\frac{9}{1000}}$ you can apply the property mentioned before. Then:

$5^{(9+\frac{9}{10}+\frac{6}{100}+\frac{9}{1000})=5^{9.969}$

(It is the equivalent expression)

B. Add the exponents:

$5^9*5^{(\frac{9}{10}+\frac{9}{10}+\frac{6}{1000})=5^{10.806}$

(It is not the equivalent expression)

C. For $5^9*5^{\frac{96}{10}}*5^{\frac{9}{100}}}$ you can apply the property mentioned before. Then:

$5^{(9+\frac{96}{10}+\frac{9}{100})=5^{18.69}$

(It is not the equivalent expression)

D. We know that $5^{9.969}=9,290,347.808$ and we maje the addition indicated in this option, we get:

$5^9+5^{\frac{9}{10}}+6^{\frac{6}{100}}=1,953,130.37$

(It is not the equivalent expression)

6 0

4 years ago

Read 2 more answers

What is the diameter of a circle with a radius of 5.4 cm

BabaBlast [244]

Answer: 10.8 cm.

Step-by-step explanation: The diameter of a circle is 2*radius. 2*5.4 = 10.8 so the answer is 10.8 cm.

5 0

3 years ago

What 2 numbers add up to 23 and multiply to -126

Pie

I don't think that's possible.

6 0

4 years ago

50 points for whoever answers the right answer

Olin [163]

Answer:

128

Step-by-step explanation:

Supplementary means they sum to 180, and it's also a straight line. 180-49 = 131. 131-3 = 128, or x.

6 0

2 years ago

Read 2 more answers