Question

There is a right angled triangle XOY right angled and angle O. M and N are mid points of OX and OY respectively. Given that XN = 19cm and YM = 22cm. Find XY.

Answer 1

In a right-angled triangle XOY, with right angle at O, let M and N be the midpoints of legs OX and OY, respectively. If XN = 19 cm and YM = 22 cm , we need to find the length of XY.

We can use the Pythagorean theorem to solve this problem. Let the length of OX be a and the length of OY be b. Then, from the midpoint theorem, we know that XN = (1/2)b and YM = (1/2)a.

Using the Pythagorean theorem, we have:

a^2 + b^2 = OX^2 + OY^2 = XY^2

Substituting XN and YM in terms of a and b, we get:

(1/4)b^2 + (1/4)a^2 = (1/2)XY^2

Substituting the given values of XN and YM, we get:

19^2 + 22^2 = (1/2)XY^2

Simplifying, we get:

XY^2 = 865

Taking the square root of both sides, we get:

XY = sqrt(865) = 29.4 cm (approx.)

Therefore, the length of XY is approximately 29.4 cm.

Explanation: