Find the base area of a rectangular pyramid whose pyramid height is 5 cm and slant height of one side of the base is 13 cm and another side of the base is 7 cm. a.  92√6 cm^2  b. 96√6 cm^2  c. 180√6 cm^2d. 100√6 cm^2e. 198√6 cm^2

Let
x> the larger side of the rectangular base
y> the smaller side of the rectangular base

we know that
Applying the Pythagoras theorem

for the larger side of the base
slant height =13 cm
h=5 cm
13²=5²+(x/2)²> (x/2)²=13²-5²> 144
(x/2)²=144> x/2=12> x=24 cm

for the smaller side of the base
slant height =7 cm
h=5 cm
7²=5²+(y/2)²> (y/2)²=7²-5²> 24
(y/2)²=24> y/2=√24> y=4√6 cm

the area of the base is
24*4√6> 96√6 cm²

the answer is the option
b. 96√6 cm^2 

Cdoes not have two variables