23 In A4BC mi90 and the length of the hypotenuse is 10 If on

23. In A4BC, mi-90° and the length of the hypotenuse is 10. If one leg is twice as long as the other leg, find the length of the shorter leg. Express answer as a simplified square root.

Solution

<c = 90\'

so this is a right trianle and by pythagoras algorithm for right angle triangle

hypotenus² = a² + b²

where a and b are other legs of triangle than hypotenus.

let a is shortest leg, length of leg a is x

it is given that b is double of a, so b = 2*a

and h = 10 given

so by algorithm,

10² = a² + b²

=>100 = x² + (2x)²

=> 100 = 5 x²

=> x² = 20

so x = sqrt(20 ) = 4.47

so a = 4.47 shortest leg, answer

and b = b = 8.94

hope this helps!

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