Question

the longest leg is
select one:
a. 20
b. 5
c. $10\sqrt{3}$
d. $5\sqrt{3}$

simplify $\sqrt{40}$
select one:
a. $4\sqrt{10}$
b. 4
c. 20
d. $2\sqrt{10}$

Explanation:

Step1: First question (missing context note)

Note: The first question about the "longest leg" is incomplete as no triangle/figure details are provided. However, assuming it refers to a 30-60-90 triangle with hypotenuse 20 (a common problem setup):
In a 30-60-90 triangle, the sides follow the ratio $1:\sqrt{3}:2$ (short leg : long leg : hypotenuse). If hypotenuse = 20, short leg = $\frac{20}{2}=10$, so long leg = $10\sqrt{3}$.

Step2: Simplify $\sqrt{40}$

Factor 40 into perfect square and remainder: $\sqrt{40}=\sqrt{4\times10}$
Apply square root property: $\sqrt{4\times10}=\sqrt{4}\times\sqrt{10}=2\sqrt{10}$

Answer:

First question (assuming standard 30-60-90 triangle with hypotenuse 20): c. $10\sqrt{3}$
Second question: d. $2\sqrt{10}$