Question

the hypotenuse of a triangle is 6.5cm and its area is 7.5 cm .calculate the lengths of its perpendicular sides​

Answer 1

Answer:

First area of right angled triangle is:

1/2×base(b) ×height(h).

The base and height always refer to the other two sides except the hypotenuse.

So  12   ×   b   ×   h   =   7.5  

Multiplying both sides by 2

bh   =   15  

Now by Pythagoras theorem

6.52  =  b2+h2  

42.25=(b+h)2−2bh  

Substituting bh = 15

42.25=(b+h)2−30  

Adding 30 on both sides

72.25=(b+h)2  

Rooting both sides

8.5=b+h  

Now bh = 15

or b =  15h  

Substituting the above value of b in b+h=8.5

15h+h=8.5  

15−8.5h+h2=0  

15−6h−2.5h+h2=0  

On solving h can be either 6 or 2.5

Now b =  15h=2.5cm (for h=6cm) or  6cm (for h=2.5cm)

So b is 2.5 cm and when h is 6 cm

And b is 6 cm when h is 2.5cm