Thread: How do I do number 7

For number 7 I only got the first part which the answer is DE =15

But I dont' know how to get part ii and part iii

Geometry Homework5

Hi yitsongg!

It is cute how they say please everywhere. First note the triangles ADE and ABC are similar. So their corresponding sides have lengths in the same ratio.
(i) 10/(4+2) = DE/2 so DE = 10/3 (which is not equal to 15)

(ii) intuitively, the sides of the ABC are (4+2)/2 = 3 times longer than sides of ADE, so the area of ABC is 3^2=9 times bigger.
More precisely, draw the altitude from the vertex A to BC. Mark P the intersection of the altitude with DE and Q the intersection of the altitude with AB. By similarity of triangles APD and AQB you have AP/AQ = AD/AB = 1/3.
Now the area of ABC is equal to BC*AQ/2 = DE*3*AP*3/2 = (DE*AP/2)*9 = m*9.

(iii) why new symbol for something already denoted by m?
The area of DECB is the area of ABC minus the area of ADE. So use (ii) to get the result.