Chapter E, Problem 8.2EX

To determine

To find the altitude of the right angled triangle.

Answer to Problem 8.2EX

Option (c) $5\sqrt{30}$ is correct.

Explanation of Solution

Given information: The altitude to the hypotenuse of a right triangle divides the hypotenuse into segment $25cm$ and $30cm$ long,

Options,

a. $15\sqrt{3}$

b. $15\sqrt{5}$

c. $5\sqrt{30}$

d. $5\sqrt{55}$

Calculation: The required solutions is obtained as,

From figure,

  $\begin{array}{l}{\left(AB\right)}^2={\left(25\right)}^2+x^2\\ {\left(AB\right)}^2=x^2+625\\ {\left(BC\right)}^2=x^2+900\\ x^2+625+x^2+900={\left(55\right)}^2\\ 2x^2+1525=3025\\ 2x^2=1500\\ x^2=750\\ x=5\sqrt{30}\end{array}$

Therefore, Option (c) $5\sqrt{30}$ is correct.