Question

PLEASE help!! Use the Pythagorean Theorem to find x!!

Answer 1

we calculate the side of the triangle of dimensions 25 and 16

25²=c²+16²

c²=25²-16²

c=√369=3√41

we calculate x :

22²=x²+ (3√41)²

22²=x²+369

x²=22²-369

x²=115

x=√115

Answer 2

`\sf x = √(115) \textsf{ or } 10.72`

Explanation:

The Pythagorean theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In other words, if a triangle has a right angle, then the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides.

The Pythagorean theorem can be written as an equation:

`\sf c^2 = a^2 + b^2`

In this case:

We need to use it twice.

For upper right angled triangle.

longest side(c) = 25

base side(a) = 16

another side be (b)

By using Pythagorean theorem:

we can say that:

`\sf 25^2= 16^2+b^2`

`\sf 625 - 256 = b^2`

`\sf b= √(369)`

`\sf b = 3√(41)`

Therefore, another side of the upper triangle is
`\sf 3√(41)`.

Now

In lower right angled triangle:

longest side(c) = 22

base side(a) = x

another side(b)=
`\sf = 3√(41)`

By using Pythagorean theorem:

we can say that:

`\sf 22^2= x^2+(3√(41))^2`

`\sf 484 = x^2 +369`

`\sf x^2 = 484-369`

`\sf x^2 = 115`

`\sf x = √(115)`

Therefore, value of x is:

`\sf x = √(115) \textsf{ or } 10.72`