Chapter 11.2, Problem 29WE

(a)

To determine

To Find: The ratios of Area of $\Delta QRTand\Delta QTS$ .

Answer to Problem 29WE

  $2:3$

Explanation of Solution

Given:

  

Area of triangle $QRT$

  $\begin{array}{l}b=RT=12\\ h=h\\ A=\frac{1}{2}bh\\ A=\frac{1}{2}(12)(h)\\ A(QRT)=6h\end{array}$

Now

Area of triangle $QTS$

  $\begin{array}{l}b=TS=18\\ h=h\\ A=\frac{1}{2}bh\\ A=\frac{1}{2}(18)(h)\\ A(QTS)=9h\end{array}$

Now

Ratio of Area of $\Delta QRTand\Delta QTS$ .

  $\frac{A(\Delta QRT)}{A(\Delta QTS)}=\frac{6h}{9h}=\frac{2}{3}=2:3$

Hence, the ratio is $2:3$

(b)

To determine

To Find: The length of altitude from $StoQR$ .

Answer to Problem 29WE

  $20$

Explanation of Solution

Given: If the area of $QRSis240$

  

Area of triangle $QRS$

Let the altitude be $x$

  $\begin{array}{l}b=QR=24\\ h=x\\ A=\frac{1}{2}bh\\ A=\frac{1}{2}(24)(x)\\ A(QRS)=12x\\ 240=12x\\ x=20\end{array}$

Hence, altitude from $StoQR$ . is $20$