Question

ABCD is a rectangle if the diagonals AC and BD meet at e , AE = 5 x - 7 cm and de = 3 X + 9 CM then find the value of AC + BD​

Answer 1

Step-by-step explanation:

AE=5x-7

we know that,

AE=1/2AC

thus, 1/2AC=5x-7

AC=10x-14-------(1)

again, DE=3x+9

we know that,

DE=1/2BD

thus, 1/2BD=3x+9

BD=6x+18------(2)

adding 1 and 2 we get,

AC+BD=16x +4

=4(4x+1)

Answer 2

$A E=5 x-7$

$\text { we know that, }$

$\mathrm{AE}=\frac{1}{2AC}$

$\text { thus, } \frac{1}{2AC} =5 x-7$

$A C=10 x-14$

$\text { again, } \mathrm{DE}=3 x+9$

$\text { we know that, }$

$\mathrm{DE}=\frac{1}{2} \mathrm{BD}$

$\text { thus, } \frac{1}{2} \mathrm{BD}=3 x+9$

$B D=6 x+18$

$by \text { adding }$

$\begin{array}{l}A C+B D=16 x+4 \\=4(4 x+1)\end{array}$

The value of AC + BD=4(4x+1)​