Answer:
The length of the hypotenuse is 2 square root of 13 ⇒ c
Step-by-step explanation:
The rule of the area of the right triangle is A =  × leg1 × leg2, where
 × leg1 × leg2, where
leg1 and leg2 are the sides of the right angle
∵ The area of a right triangle is 12 in²
∵ The ratio of the length of its legs is 2: 3
→ Let leg1 = 2x and leg2 = 3x
∵ leg1 = 2x and leg2 = 3x
→ Substitute them in the rule of the area above
∴ 12 =  × 2x × 3x
 × 2x × 3x
∵ 2x × 3x = 6x²
∴ 12 =   × 6x²
 × 6x²
∴ 12 = 3x²
→ Divide both sides by 3 to find x²
∴ 4 = x²
→ Take √ for both sides
∴ x = 2
→ Substitute x in the expressions of leg1 and leg2 to find them
∴ leg1 = 2(2) = 4 inches
∴ leg2 = 3(2) = 6 inches
∵ hypotenuse =  
 
∴ hypotenuse = 
∵ The simplest form of  = 2
 = 2
∴ The length of the hypotenuse = 2 inches
 inches
 
        
             
        
        
        
Answer:
a - 13/30 
Step-by-step explanation:
2/5 +x = 5/6 
2/5 + x -2/5 = 5/6 - 2/5 
x = 13/30