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 = [tex]\frac{1}{2}[/tex] × 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 = [tex]\frac{1}{2}[/tex] × 2x × 3x
∵ 2x × 3x = 6x²
∴ 12 = [tex]\frac{1}{2}[/tex] × 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 = [tex]\sqrt{(leg1)^{2}+(leg2)^{2}}[/tex]
∴ hypotenuse = [tex]\sqrt{(4)^{2}+(6)^{2}}=\sqrt{16+36}=\sqrt{52}[/tex]
∵ The simplest form of [tex]\sqrt{52}[/tex] = 2[tex]\sqrt{13}[/tex]
∴ The length of the hypotenuse = 2[tex]\sqrt{13}[/tex] inches
