Question

The hypotenuse of a right triangle is 41 & the difference between the other a sides is 31- Find the other 2 sides.​

Answer 1

Answer:9, 40

Step-by-step explanation: Sometimes to solve geometric problems, quadratic formula can help a lot. See the attachments to find more details.

Hope it helps.

Answer 2

Given:

The hypotenuse of a right triangle is 41 & the difference between the other sides is 31

To Find:

Find the other 2 sides.​

Solution:

Let the sides be a and b, so it is said that the difference between them is 31, so we write that

a-b=31            -(1)

Now using the Pythagoras theorem we can write,

$a^2+b^2=41^2$      -(2)

Now squaring both sides of equation 1 and putting the value of equation 2 in equation 1 we have,

$(a-b)^2=31^2\\a^2+b^2-2ab=31^2\\2ab=41^2-31^2\\2ab=10*72\\ab=360$

Now we have two equations,

a-b=31

ab=360

Now substituting the value of b in equation 1 we have,

$a-b=31\\a-\frac{360}{a} =31\\a^2-360=31a\\a^2-31a-360=0$

Now using the quadratic formula to find the values of a, we have,

$a=\frac{31\pm \sqrt{961+1440} }{2}\\=\frac{31\pm 49}{2}\\=40,-9$

So we will consider the positive value of a, now taking a=40 the value of b is

ab=360

b=360/40

b=9

So the values of a and b are 40 and 9 respectively,

Hence, the other two sides are 40 and 9.