Question

What is the length of BC?

A)5

B)20

C)15

D)30

Answer 1

What is the length of _?

Answer 2

BC

Answer 3

Well, just an idea, but if you subtract the areas you get the area of the trapezium...?

Answer 4

30-7.5?

Answer 5

Yeah, wait a second.

Answer 6

THATS 22.5

Answer 7

You are right. OK, so 22.5 is the area of trapezium XYCB.

Answer 8

Do you know the formula of the area of a trapezium by any chance?

Answer 9

A=1/2h(b1+b2)

Answer 10

Great! Now, let's leave that there for a while. We'll come back to this.

Answer 11

All right. Let's start looking at \(\triangle AXY\) now. The area of the triangle is given as \(7.5\). The formula of the area is \(\dfrac{1}{2}\times b \times h\). The base is \(XY = 5\).

So, \(\dfrac{1}{2} \times 5 \times h = 7.5 \Rightarrow h = 3\). Do you get that till here?

Answer 12

So its 5?

Answer 13

Nope. Do you get how the height of AXY is 3?

Answer 14

I'll continue if yes.

Answer 15

yes i got how you got the height.

Answer 16

Now, let's look at \(\triangle ABC\). The area is \(30\), which is equal to \(\dfrac{1}{2}\times BC \times H\). Hence, \(BC \times H = 60\)

Answer 17

30?

Answer 18

Note that \(H\) is the height of ABC. Now, area of XYBC is \(\dfrac{h_{XYBC}}{2}\left(BC + 5\right) = 22.5\). The height of XYBC is \(H - h = H - 3\). We are left with\[\dfrac{H - 3}{2}\left(BC + 5\right) = 22.5 ~ ~ ~ and ~ ~ ~ BC \times H = 60\]

Answer 19

Two equations, two variables. Oh, and I don't know the answer yet either. Too lazy to solve it. :P

Answer 20

are you serious?

Answer 21

Yeah, but this should get you the answer.

Answer 22

i dont know how but ok thanks