Question

1. In
ABC
if DE 11 AB AD=8x+9
DE 11 AB AD=8x+9 = x+3 BE =
D3
3x+7 and co= x then and the
cwhefr​

Answer 1

Given — a:b = 5:9 and b:c = 4:7

Now, write it in the tabular form like this-

a : b : b

b' : b' : c *

Now multiply the numbers in the columns like this —

ab' : bb': bc

So in this way, the answer to the question is 5*4 : 9*4 : 9*7 = 20:36:63

Note: In both the ratios , b is different so don't that's why I have used b and b'. b represents the 2nd term of first ratio and b' represents the 1st term of second ratio. This is a really useful method. It can also be used in more than two ratios like a:b:c:d.

Thanks!!

Answer 2

Given,

DE//AB

$\frac{AD}{DC} = \frac{BE}{EC} \\ \\ \frac{8x + 9}{x + 3} = \frac{3x + 4}{x} \\ \\ {8x}^{2} +9x= {3x}^{2} +13x+12 \\ \\ {5x}^{2} −4x−12=0 \\ \\ {5x}^{2} −10x+6x−12=0 \\ \\ 5x(x−2)+6(x−2)=0 \\ \\ (5x+6)(x−2)=0 \\ \\ x = \frac{ - 6}{5} \: and \: 2$

Therefore x is 2.