Question

Choose the best answer:

Answer 1

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 = $\frac{1}{2}$ × 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 = $\frac{1}{2}$ × 2x × 3x

∵ 2x × 3x = 6x²

∴ 12 =  $\frac{1}{2}$ × 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 = $\sqrt{(leg1)^{2}+(leg2)^{2}}$

∴ hypotenuse = $\sqrt{(4)^{2}+(6)^{2}}=\sqrt{16+36}=\sqrt{52}$

∵ The simplest form of $\sqrt{52}$ = 2$\sqrt{13}$

∴ The length of the hypotenuse = 2$\sqrt{13}$ inches