Choose the best the area of a right triangle is 12in^2. the ratio of the length of its legs is 2:3. Find the length of the hypotenuse.
a) square root is 13 in
b) 26 inches
c) 2 square root of 13
d) 52 inches
e) 4 square root of 13

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 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 = 6x²

∴ 12 =   × 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

∴ The length of the hypotenuse = 2 inches

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

b.my answer is b.

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