Question

The perimeter of a right triangle is 60. the length of the perpendicular to the hypotenuse is 12 what is the area?

Answer 1

Refer to the attached image.

Consider the given triangle ABC right angles at B.

Given : AB = 12 and Perimeter is 60 cm

To find: Area of triangle ABC

Solution: Let the side AC ='x' and BC='y'.

Since perimeter is 60 cm

Therefore, x+y+12 = 60

So, x+ y = 48

So, x = 48-y (Equation 1)

Now, consider right triangle ABC,

By Pythagoras theorem,

$AC^{2}=AB^{2}+BC^{2}$

$x^{2}=12^{2}+y^{2}$

$x^{2}=144+y^{2}$

Substituting the value of 'x' from equation 1 in the above equation.

$(48-y)^{2}=144+y^{2}$

$2304+y^{2}-96y=y^{2}+144$

$96y=2160$

y=22.5 cm

Now, area of right angled triangle = $\frac{1}{2} \times base \times height$

$=\frac{1}{2} \times y \times 12$

$=\frac{1}{2} \times 22.5 \times 12$

= 135 square cm.

So, the area of triangle is 135 square cm.