Question

The hypotenuse of a right triangle is 25 cm and its sides containing the right angle differ
by 5 cm. Find the sides of the triangle which contain the right angle. ​

Answer 1

Step-by-step explanation:

c²=a²+b²

(25 cm)²=(5 cm)² + b²

(25 cm)² - (5 cm)² = b²

b² = 625 cm² - 25 cm²

b² = 600 cm²

take the square root of both sides

√b² = √600 cm²

b = 10√6 cm ANSWER

Answer 2

Answer:

Have a look in the diagram too:

Given: side BC = 25 cm (because it is hypotenuse)

Let side AB = x

ATQ:  difference between AB and AC = 5

So, AC = x - 5

Now: Applying pythagoras theorem

BC² = AB² + AC²

(25)² = x² + (x - 5)²

625 = x² + x² + 5² - 2(5x)

625 = 2x² + 25 - 10x

0 = 2x² - 10x + 25 - 625

0 = 2x² - 10x - 600

Taking 2 as common:

0 = 2[x² - 5x - 300]

0/2 = x² - 5x - 300

0 = x² - 5x - 300

Now .... solving this quadratic equation we get:

0 = x² -20x + 15x - 300

0 = x(x-20) + 15(x-20)

0 = (x-20)(x+15)

So value of x:  x - 20 = 0                               x+15 = 0

                       x = 20,          or                            x = -15

But value of x cannot be in negative, so x = 20

Now: side AB = 20cm

and, AC = 20 - 5

             = 15 cm

Step-by-step explanation:

Hope it helps :)