Question

the altitude of a right triangle is 7cm less than its base. if the hypotenus is 13 cm the other two sides of triangle are equal to:​

Answer 1

Answer:

12cm , 5 cm

Step-by-step explanation:

Let the base of the triangle be x, thus the altitude should x - 7.

Given, hypotenuse = 13

using Pythagoras theorem,

⇒ x² + (x - 7)² = 13²

⇒ x² + x² + 49 - 14x = 169

⇒ 2x² - 14x + 49 - 169 = 0

⇒ 2x² - 14x - 120 = 0

⇒ x² - 7x - 60 = 0

⇒ x² - 12x + 5x - 60 = 0

⇒ x(x - 12) - 5(x - 12) = 0

⇒ (x - 12)(x + 5) = 0

x can't be -ve, so x = 12.

Hence,

Base = x = 12 cm

Altitude = x - 7 = 12 - 7 = 5 cm

Answer 2

Given :-

The altitude of a right triangle is 7cm less than its base. if the hypotenus is 13 cm

To Find :-

Other side

Solution :-

Let the altitude be a and base be b

a = b - 7 (1)

c² = a² + b²

(13)² = a² + b²

169 = (b - 7)² + b²

Apply identity ⇒ (a - b)² = a² - 2ab + b²

169 = (b)² - 2(b)(7) + (7)² + b²

169 = b² - 14b + 49 + b²

169 - 49 = b² - 14b + b²

120 = 2b² - 14b

120/2 = 2b² - 14b/2

60 = b² - 14b

0 = b² - 7b - 60

0 = b² - (12b - 5b) - 60

0 = b² - 12b + 5b - 60

0 = b(b - 12) + 5(b - 12)

0 = (b + 5)(b - 12)

b + 5 = 0

b = -5

Or,

b - 12 = 0

b = 12

Since, Length can not be negative b = 12

Using 1

a = b - 7

a = 12 - 7

a = 5