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Question
The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is ______.
Options
25 cm2
28 cm2
30 cm2
40 cm2
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Solution
The base and hypotenuse of a right triangle are respectively 5 cm and 13 cm long. Its area is 30 cm2.
In right angled triangle ABC having base 5 cm and hypotenuse 13 cm we are asked to find its area
Using Pythagorean Theorem
`AB^2 = AC^2 + BC^2`
Where, AB = hypotenuse = 13 cm, AC = Base = 5 cm, BC = Height
`(13)^2 = (5)^2 + BC^2`
`169 = 25 + BC^2`
`BC = sqrt( 169-25)`
BC = 12 cm
Area of a triangle, say A having base 5 cm and altitude 12 cm is given by
`A = 1/2 (" Base" xx " Height ")`
Where, Base = 5 cm; Height = 12 cm
`A = 1/2 (5 xx 12)`
A = (5 × 6)
A = 30 cm2
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