the area of a right angled triangle is 30 sq cm and..., Area, General Mathematics

Question:The area of a right angled triangle is 30 sq.cm and the length of its hypotenuse is 13 cm. The length of the shorter leg is :

A 4 cm 
B 5 cm 
C 6 cm 
D 7 cm

/98

+ AnswerB

+ ExplanationLet the order sides be x and y Then,

`x^2 + y^2 = (13)^2`

`= 169.` Also, `1/2 xy = 30 => xy = 60`

`:. (x + y) = sqrt(x^2 + y^2) + 2xy`

`= sqrt(169 + 120)`

`= sqrt(289)`

`= 17`

`(x - y) = sqrt((x^2 + y^2)) - 2xy`

`= sqrt(169 - 120)`

`= sqrt(49)`

`= 7`

Solving x + y = 17, x - y = 17, x - y = 7, we get x = 12 x = 12 and y = 5

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