Question

In ∆ABC with m∠C = 90° the sides satisfy the ratio BC:AC:AB = 4:3:5. If the side with middle length is 12 cm, find: 1) The perimeter of ∆ABC; 2) The area of ∆ABC; 3) The height to the hypotenuse.

Answer 1

The Hypotenuse AB = 20cm

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Answer 2

*The side with the middle length is 12cm, therefore BC must be 12 cm

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Ratio
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BC:AC:AB
4 : 3 : 5

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Find 1 share
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Given that BC = 12 cm
4 shares = 12 cm
1 share = 12 ÷ 4 = 3cm

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Find AC (4 shares)
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3 shares = 3 x 3 = 9 cm
BC = 9cm

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Find AB (5 shares)
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5 shares = 5 x 3 = 15cm
AB = 15cm

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Length
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BC : AC : AB
12cm : 9cm : 15cm

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Perimeter
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12 + 9 + 15 = 36cm

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Answer: The perimeter is 36cm
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Area
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1/2 x 9 x 12 = 54cm²

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Answer: Area = 54cm²
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Given that the biggest ratio is AB
⇒AB is the hypotenuse
AB = 15 cm

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Answer: Hypotenuse = AB = 15cm
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