+0

0
219
1

iN THE FIGURE AB:BC=4:3 AND BD//CE and area of  triangle ADB is 24cm^2 and the area of the trapezium BCED is 60 cm^2, find Area of triangle ADE

Guest Feb 23, 2015

#1
+889
+10

Draw a line through A parallel to DB and EC and a line through C to meet this line in a right angle. Call the point of intersection F. Extend DB to meet the new line through C at G.

Since AB:BC = 4:3, by similar triangles FG:GC = 4:3, so let FG = 4a and GC = 3a, for some constant a.

Let the length of CE = p and the length of BD =q.

The area of the parallelogram is 60, so (p + q).3a/2 = 60, so,    pa + qa = 40................(1)

The area of the triangle ABD is 24, so,  q.4a/2 = 24, so                     qa =  12................(2)

From (1) and (2), pa = 28.

The area of the big triangle ACE = p.7a/2 = 28*7/2 = 98,

in which case the area of the triangle ADE = 98 -24 - 60 = 14.

Bertie  Feb 23, 2015
Sort:

#1
+889
+10

Draw a line through A parallel to DB and EC and a line through C to meet this line in a right angle. Call the point of intersection F. Extend DB to meet the new line through C at G.

Since AB:BC = 4:3, by similar triangles FG:GC = 4:3, so let FG = 4a and GC = 3a, for some constant a.

Let the length of CE = p and the length of BD =q.

The area of the parallelogram is 60, so (p + q).3a/2 = 60, so,    pa + qa = 40................(1)

The area of the triangle ABD is 24, so,  q.4a/2 = 24, so                     qa =  12................(2)

From (1) and (2), pa = 28.

The area of the big triangle ACE = p.7a/2 = 28*7/2 = 98,

in which case the area of the triangle ADE = 98 -24 - 60 = 14.

Bertie  Feb 23, 2015

### 17 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details