Question

5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find
the other two sides.​

Answer 1

Answer:

The other two sides are 12 cm and 5 cm.

Step-by-step explanation:

Given :-

• The altitude of a right triangle is 7 cm less than its base.
• The hypotenuse is 13 cm.

To find :-

• Altitude and base of the right triangle.

Solution :-

Let the base of the right triangle be x cm.

★ The altitude of a right triangle is 7 cm less than its base.

Then,

• Altitude = (x-7) cm

Pythagoras Theorem :

${\boxed{\sf{Altitude^2+Base^2=Hypotenuse^2}}}$

→ (x-7)² + x² = 13²

→ x² - 14x + 49 + x² = 169

→ 2x² - 14x +49 -169 = 0

→ 2x² - 14x - 120=0

→ 2(x² - 7x - 60) = 0

→ x² - 7x -60 = 0

→ x² - (12-5)x - 60 = 0

→ x² - 12x + 5x -60 = 0

→ x(x-12) + 5(x-12) = 0

→ (x-12)(x+5) = 0

Either,

x - 12 = 0

→ x = 12

Or,

x+5 = 0

→ x = -5 [ impossible]

• Base of the right triangle = 12 cm

Then,

• Altitude = (12-7) = 5 cm

Answer 2

Answer:

Let base be x cm , then altitude will be (x-7) cm.

Now ,

By using pythagoras theorem-

132 = x2 + (x-7)2

169 = x2 + x2 + 49 - 14x

2x2 - 14x - 120 = 0

x2 - 7x - 60 = 0

x2 - 12x + 5x - 60 = 0

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

Hence x = 12

sO , Altitude is 5 cm

AND. ,