Question

Pythagoras
Round the answer to 1 decimal place

Answer 1

To one decimal place, x = 32.4 cm

Explanation:

We can find x by first finding the middle length using the triangle on the right,

let the middle length be c

for the triangle on the right,

hypotenuse = 50 cm

base = 20 cm

Using the Pythagorean theorem,

`(hypotenuse)^2=(base)^2+(height)^2`

Putting values, we get,

`50^2 = 20^2+c^2\\c^2 = 50^2-20^2\\c^2=2500-400\\c^2=2100\\c=10√(21)`

so, c = 10(sqrt(21))

For the triangle on the left

Now,

For the triangle on the left, the middle length is the hypotenuse,

and we see that both the base and the height are equal (from the small dashes on these sides). i.e base = height = x

So, applying the theorem, we get,

`c^2 = x^2+x^2\\c^2=2x^2\\(10√(21))^2=2x^2\\ 2100=2x^2\\2100/2=x^2\\1050 = x^2\\x= 5√(42)`

Now, to 1 decimal place, x is,

x = 32.4 cm