Question #2312f

1 Answer
Feb 15, 2018

See explanation.

Explanation:

If we write the diagonals as #d_1# and #d_2# then using the Pythagorean theorem we can write that:

#(d_1/2)^2+(d_2/2)^2=20^2#

#(d_1/2)^2+(3/8d_1)^2=20^2#

#d_1^2/4+9/64d_1^2=400#

#(16d_1^2+9d_1^2)/64=400#

#25/64d_1^2=400#

#5/8d_1=20#

#d_1=32#

Now we can use #d_2=3/4d_1=24#

Finally we can calculate the area:

#A=1/2d_1d_2=1/2*24*32=12*32=384#

Answer: The area of the rombus is #A=384m^2#.