Question

The legs of a right triangle are in the ratio of 3:4 and its area is 1014 sq.cm. Find its hypotenuse.

Answer 1

Let it's leg be 3x and 4x. Then,

according to question,

Area of right angle triangle = 1/2 × 3x × 4x

1,014 = 6x^2

1,014/6 = x^2

√169 = x

13 cm = x

Hence, first side = 3×13 = 39 cm

second side = 4×13 = 52 cm.

We know that

H^2 = P^2 + B^2

H^2 = 39^2 + 52^2

H^2 = 1521 + 2704

H = √4225

H = 65 cm.

Hence, the hypotenuse is 65 cm.

 

Answer 2

Let the base and perpendicular of the right angled triangle be 3x and 4x respectively.

Area of the right angled triangle = 1/2 × base × height

1014 sq. cm = 1/2 × 3x × 4x

1014 × 2 / 12 = x^2

169 = x^2

√169 = x

x = 13

By Pythagoras theorem:

(H) ^2 = (P) ^2 + (B) ^2

(H) ^2 = (4x) ^2 + (3x) ^2

(H) ^2 = 16x^2 + 9x^2

(H) ^2 = 25x^2

H = √25x^2

H = 5x - ( 1 )

Putting the value of x=13 in equation 1 , we get :

H = 5×13 = 65cm

Ans : Hypotenuse = 65cm

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