Chapter 11.7, Problem 21PSC

To determine

To calculate:Theratio of area of triangle ABDandarea of triangle BCD .

Answer to Problem 21PSC

Theratiois $5:6$ .

Explanation of Solution

Given information:

A trapezoidABCD, SideAB = 16 ,

Side BC = 18 ,

Side CD = 17 ,

Side AD = 15 .

Formula used:

Area of triangle: $A=\frac{1}{2}\times b\times h$

b = base of triangle

h = height of triangle

Calculation:

  

The height of both triangles is same because the bases of trapezoid are parallel.

The ratio of two triangles is as follows:

  $\begin{array}{l}\frac{A(△ABD)}{A(△BCD)}=\frac{\frac{1}{2}\times AD\times AB}{\frac{1}{2}\times BC\times CD}\\ \frac{A(△ABD)}{A(△BCD)}=\frac{\frac{1}{2}\times 15\times h}{\frac{1}{2}\times 18\times h}\\ \frac{A(△ABD)}{A(△BCD)}=\frac{15}{18}\\ \frac{A(△ABD)}{A(△BCD)}=\frac{5}{6}\end{array}$