Question

Hello, I am being asked to look for the length of the altitude of a hypotenuse?

Answer 1

D.14

Explanation

here we have 3 rigth triangles:

so

Step 1

a)from green triangle :using the Pythagorean theorem we have

$\begin{gathered} 7^2+d^2=a^2 \\ d^2=a^2-7^2\Rightarrow equation\left(1\right) \end{gathered}$

b) from blue triangle

$d^2+28^2=b^2\Rightarrow eq(2)$

c) from triangle red

$\begin{gathered} a^2+b^2=(28+7)^2 \\ a^2+b^2=1225\Rightarrow eq(3) \end{gathered}$

Step 2

now, solve the equations

a) replace the square d value fromequation(1) into equation(2)

$\begin{gathered} d^2+28^2=b^2\Rightarrow eq(2) \\ (a^2-7^2)+784=b^2 \\ a^2+784-49=b^2 \\ a^2+735=b^2 \\ \end{gathered}$

b)now, replace the square b value into equation(3) and solve for a

$\begin{gathered} a^2+b^2=1225\Rightarrow eq(3) \\ a^2+(a^2+735)=1225 \\ 2a^2+735=1225 \\ subtract\text{ 735 in both side} \\ 2a^2+735-735=1225-735 \\ 2a^2=1225-735 \\ a^2=\frac{490}{2} \\ a^2=245 \\ a=\sqrt{245} \end{gathered}$

c)finally, replace the a value in equation (1) and solve for d ( heigth )

so

$\begin{gathered} a^2-7^2=d^2\Rightarrow equation(1) \\ d^2=(\sqrt{245})^2-49 \\ d^2=245-49 \\ d^2=196 \\ square\text{ root in both sides} \\ d=\sqrt{196} \\ d=14 \end{gathered}$

therefore, the answer is

D.14

I hope this helps you