Question

What are the values of x and y?

Answer 1

Step-by-step explanation:

y is easy.

it is the Hypotenuse (baseline) of the small right-angled triangle created by the height (8) of the main triangle, the segment 6 of the main Hypotenuse and y.

so, Pythagoras :

y² = 8² + 6² = 64 + 36 = 100

y = 10

x is a bit more complex.

I think the easiest way to get it is to know that the height of a right-angled triangle to the Hypotenuse is the square root of the product of both segments of the Hypotenuse.

so, if we call the segments of the Hypotenuse a and b with a = 6, we have

x = a + b = 6 + b

height (8) = sqrt(a×b) = sqrt(6b)

therefore,

6b = height² = 8² = 64

b = 64/6 = 32/3 = 10 2/3 = 10.66666666...

so,

x = 6 + 10.66666... = 16.666666666...

round it to what is needed. e.g. 2 positions after the decimal point (hundredths) ? then it would be 10.67