Question

the length of the triangle are in the ratio 3 : 4 and its area is 1014 cm square. find the hypotenuse ​

Answer 1

Since the ratio of the legs of right angled triangle is 3 : 4.

So, suppose the legs of right angled triangle are 3x and 4x.

So area of right angle triangle = 12×3x×4x = 1014 cm2

⇒6x2 = 1014⇒x2 = 10146⇒x2 = 169⇒x = ±169−−−√ = ±13

Since the length can't be negative, so neglect x = -13.

So, x = 13

So legs of right angled triangle are 3×13 i.e. 39 cm and 4×13 i.e. 52 cm.