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Question
The legs of a right-angled triangle are in the ratio 4 : 3 and its area is 4056 cm2. Find the length of its legs.
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Solution
Area of right-angled triangle = 4056 cm2
Legs of a right-angled triangled are in the ratio i.e. 4 : 3
Let one leg (Base) = 3x
Then second leg (altitude) = 4x
Area =`1/2xx"Base"xx"Altitude"`
= `1/2xx3"x"xx4"x"` = 6x2
∴ 6x2 = 4056
x2 = `4056/6` = 676
x = `sqrt676=sqrt(26xx26)`
∴ x = 26 cm
∴ One leg (base) = 3x = 3 × 26 = 78 cm
and second leg (altitude) 4x = 4 × 26 = 104 cm
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