Question

Find all sides of a right triangle whose perimeter is equal to 60 cm and its area is equal to 150 square cm

Answer 1

Answer:

15cm by 20cm by 25cm

Step-by-step explanation:

Let the sides of the right angle be x, y and h

x is the breadth

y is the height

h is the hypotenuse

Perimeter = x + y + h

x + y +h  = 60

x+y = 60-h .... 1

If its area is equal to 150 square cm, then;

Area = 1/2 * base * height

Area = 1/2 *x * y

xy/2 = 150

xy = 300 ....2

According to pythagoras theorem;

x² + y² = h²

On expanding x² + y²

x² + y² = (x+y)² - 2xy

The equation becomes

(x+y)² - 2xy = h² ... 3

Substitute equation 1 and 2 into 3;

From 3;

(x+y)² - 2xy = h² ... 3

(60-h)² - 2(300) = h²

3600-120h + h² - 600 = h²

3600-120h - 600 = 0

-120h = 600-3600

-120h = -3000

h = 3000/120

h = 25cm

Recall that x+y+h = 60

x+y+25 = 60

x+y = 60 - 25

x+y = 35 ... 4

From equation 2;

xy = 300

x = 300/y ..... 5

Substitute 5 into 4;

300/y + y = 35

(300+y²)/y = 35

300+y² = 35y

y²-35y + 300 = 0

y²-20y-15y + 300 = 0

y(y-20)-15(y-20) = 0

y-20 = 0 and y - 15 =0

y = 20 and 15

since x+y = 35

x + 20 = 35

x = 35 - 20

x = 15

Hence the sides of the triangle are 15cm by 20cm by 25cm