Question

26 The side of a right argle triangle are 52 & (32-1) cm respectively If its nahe area is 60cm, find its Perimeter​

Answer 1

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Let ABC be a right angled triangle with right angle at B

let AB=5x and BC=3x−1.

Then, area =△ABC=1/2 (Base×Height))

⇒60=1/2 (AB×BC)

⇒60=1/2×5x(3x−1)

⇒120=5x(3x−1)

⇒3x^2−x−24=0

⇒3x^2−9x+8x−24=0

⇒(x−3)(3x+8)=0

⇒x=3 or 3x+8=0

⇒x=3 or x=−8/3⇒x=3

AB=5x=5×3=15cm and BC=(3x−1)=(3×3−1)=8cm

Now, AC^2+AB^2+BC^2

⇒AC^2=15^2+8^2

⇒AC^2

=289

⇒AC=17cm

Hence, hypotenuse =17cm