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Olegator [25]
2 years ago
13

Choose the best answer:

Mathematics
1 answer:
Oksi-84 [34.3K]2 years ago
3 0

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

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