Question

QN07: The altitude of a right Ais 7cm less than its base. If the hypotenuse is 13cm.
find the other two sides (7cm)​

Answer 1

Given

The altitude of a right is 7cm less than its base. If the hypotenuse is 13cm.

Find out

Find the other two sides

Solution

★ Let the base of right triangle be x the altitude be (x - 7)

• Hypotenuse = 13 cm

According to the Pythagoras theorem

(hypotenuse)²=(base)²+(perpendicular)²

➟ (13)² = (x)² + (x - 7)²

Apply identity :

(a - b)² = a² + b² - 2ab

➟ 169 = x² + x² + (7)² - 2 × x × 7

➟ 169 = 2x² + 49 - 14x

➟ 169 - 49 = 2x² - 14x

➟ 120 = 2x² - 14x

➟ 2x² - 14x - 120 = 0

➟ 2(x² - 7x - 60) = 0

➟ x² - 7x - 60 = 0

Splitting middle term

➟ x² + 7x - 12x - 60x = 0

➟ x(x + 7) - 12(x + 7) = 0

➟ (x + 7)(x - 12) = 0

Either

➟ (x + 7) = 0

➟ x = - 7

Or

➟ (x - 12) = 0

➟ x = 12

★ Length can't be in negative ★

Hence,

• Base = x = 12 m
• Altitude = (x - 7) = (12 - 7) = 5m

$\rule{200}3$

Answer 2

Solution

Let the base of right triangle be x the altitude be (x - 7)

Hypotenuse = 13 cm

(hypotenuse)²=(base)²+(perpendicular)²

(13)² = (x)² + (x - 7)²

169 = x² + x² + (7)² - 2 × x × 7

169 = 2x² + 49 - 14x

169 - 49 = 2x² - 14x

120 = 2x² - 14x

2x² - 14x - 120 = 0

2(x² - 7x - 60) = 0

x² - 7x - 60 = 0

x² + 7x - 12x - 60x = 0

x(x + 7) - 12(x + 7) = 0

(x + 7)(x - 12) = 0

______________

(x + 7) = 0

x = - 7

____________

(x - 12) = 0

x = 12

______________

Base = x = 12 m

Altitude = (x - 7) = (12 - 7) = 5m