Question

ABCD is a trapezium such that ABllCD .if √AC^2+√BD^2=13cm and√AC×√BD=2√15 .then the sum of cubes of length of diagonals ABCD is.

please answer fast​

Answer 1

Given:

ABCD is a trapezium such that AB ll CD, if $\sqrt{AC^2+BD^2}=13$ and $\sqrt{AC*BD} =2\sqrt{15}$

To Find:

then the sum of cubes of the length of diagonals ABCD is

Solution:

First using the second equation given and finding the possible values of AC and BD

$\sqrt{AC*BD} =2\sqrt{15}\\AC*BD=60$

Now taking into consideration the values of AC*BD

AC*BD

1*60

2*30

3*20

4*15

5*12

6*10

now matching these values in the 1st equation

$\sqrt{AC^2+BD^2}=13\\AC^2+BD^2=169$

then only the values(5,12) satisfies the given equation

$=5^2+12^2\\=25+144\\=169$

now, finding the sum of cubes of the length of diagonals ABCD

$Sum=5^3+12^3\\=125+1728\\=1853cm$

Hence,  the sum of cubes of the length of diagonals ABCD is 1853cm.