(1/2)(2x)(h)=600, so xh=600, or x=(600/h), or x2=(360000/h2)
(360000/h2)=h2-900
360000=h4-900h2
h4-900h2-360000=0
h2+300=0
h2-1200=0
h2=1200
x2=1200-900
x2=300
x=(300)^(1/2)
base=2(300)^(1/2)
Suppose a pyramid with a square base has a height of 30 feet. The slanted
sides are four identical isosceles triangles each of which has area 600 square feet.
Find the exact length of the base sides.
Let the base=2x. Then (30)(30)+(x)(x)=(h)(h), or 900+x2=h2, or x2=h2-900.
(1/2)(2x)(h)=600, so xh=600, or x=(600/h), or x2=(360000/h2)
(360000/h2)=h2-900
360000=h4-900h2
h4-900h2-360000=0
h2+300=0
h2-1200=0
h2=1200
x2=1200-900
x2=300
x=(300)^(1/2)
base=2(300)^(1/2)