Q. 184.0( 4 Votes )

# Length of hypotenuse and perimeter of a right-angle triangle are 13 cm and 30 cm. Let us write by calculating the area of triangle.

Let the base, perpendicular and Hypotenuse of right-angled triangle be b, p and h respectively.

We know, Perimeter of right-angled triangle = b + p + h

Given, perimeter = 30 cm

b + p + h = 30

b + p + 13 = 30 [ h, hypotenuse = 13 cm]

b = 17 – p [1]

Also, we know By Pythagoras theorem in right-angled triangle

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

h2 = p2 + b2

(13)2 = p2 + (17 – p)2

169 = p2 + p2 + 289 – 34p

2p2 – 34p + 120 = 0

p2 – 17p + 60 = 0

p2 – 12p - 5p + 60 = 0

(p – 12)(p - 5) = 0

p = 12 cm or p = 5 cm

Case I: p = 12 cm

b = 17 – 12 = 5 cm

and we know, area of triangle

Case II: p = 5 cm

b = 17 – 5 = 12 cm

and we know, area of triangle

Therefore, Area of triangle is 30 cm2.

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