Question

In each of the figures given below, an altitude is drawn to the hypotenuse by a right-angled triangle. The length of different line-segment are marked in each figure. Determine x, y, z in each case.

(i)

(ii)

Answer 1

(i) is right angled triangle right angled at B

is right triangle right angled at D

is right triangle right angled at D

By canceling equation and by elimination method, we get

y canceling and by elimination method we get

Now, substituting in equation (iv) we get

Now, substituting in equation (ii) we get

Hence the values of x, y, z is

(ii) is a right triangle, right angled at Q

…… (i)

is a right triangle right angled at S

is a right triangle right angled at S

…… (ii)

Now substituting in equation (i) we get

Now substituting in equation (iii) we get

Now substituting and in equation (ii) we get

Hence the value of x, y and z are