Answer:
4 inches
Explanation:
slant height = 3, surface area = 40.
let L = length of one side (since it's a square, it will be L for each edge of the base).
surface area = base + 4 sides of triangles
= L² X 4 (0.5 X base X height)
= L² X 4(0.5 X L X 3)
= L²+ 6L.
But surface area = 40.
So L² + 6L = 40.
Subtract 40 from both sides:
L² + 6L - 40 = 0.
Use the quadratic formula:
L = ((-b ± √(b² - 4ac)) ÷ 2a)
where a is the value of the first coefficient, b is value of the second and c is value of the constant.
L = ((-6 ± √(6² - 4(1)(-40))) ÷ 2(1))
= ((-6 ± √(36 + 160)) ÷ 2)
= (-6 ± 14) ÷ 2
= (-6 + 14) ÷ 2 or (-6 - 14) ÷ 2
= 4 or -10.
So L = 4 or -10. But L is a length, so it must be positive. So L = 4.
Length = 4 inches