Kendra was asked to find the number of students who planned to attend the evening symphony performance. She was told that 40 per
cent of the 50 students planned to attend. Kendra’s work is shown below.
1 answer:
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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 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