Krishna
0

Step 1: Make a note of the given data

NOTE:  Triangle perimeter = 60

Triangle area  = 150 units^2

Find the  sides measurements

Step 2: Draw an imaginary figure and set up an equation from the given data

Triangle perimeter = 60

a + b + h = 60 ........................(1)

Triangle area  = 150 units^2

\frac{1}{2}(a*b) = 150 unit^2

ab = 300 ............................(2)

Step 3: Solve the equations (1)

a + b + h = 60

Skill 1: Rewrite the equation

as follows

a + b = 60 - h

Skill 2:   Square both sides

(a + b)2 = (60 - h)2

Skill 3:   Expand both sides

a^2 + b^2 + 2 a b = 60^2 + h^2 - 120 h

Skill 4:  Combine the equation a^2 + b^2 = h^2

with the above equation to obtain

2 a b = 60^2 - 120 h

Skill 5: a b is known to be equal to 300, hence the above

equation  becomes

600 = 60^2 - 120 h

Skill 6: Solve for h to obtain

h = 25 units

Step 4: Substitute h by 25 in the equation a + b + h = 60

a + b = 60 - 25 = 35

Step 5:  a b = 300, then [math] b = \frac{300}{a} which is substituted in the

equation a + b = 35

a + \frac{300}{a -35} = 0

Step 5 : Do the L.C.M to obtain a quadratic equation of the form

a^2 - 35a + 300 =0

Step 6: Solve the above equation to obtain two solutions

a = 20 and a = 15

The two sides of the right triangle and the hypotenuse are,

respectively, given by

15 units, 20 units and 25 units.

If you want you can check the perimeter and area given in the problem.