Question

the perimeter og a right _ angled triangle is 48 centimeters, and its area is 96 square centimeters. length of hypotenuse is 20 cm.


what is the length of the perpendicular sides?​

Answer 1

Correct Question :

The perimeter of a right angled triangle is 48 cm , and its area is 96 cm² . Length of its hypotenuse is 20 cm . What is the length of the perpendicular sides ?

Solution :

Let , In a right angled triangle ,

• B ⇔ Base
• P ⇔ Perpendicular
• H ⇔ Hypotenuse

Perimeter of a right angled triangle is sum of all its sides ,

➳ Per. = B + P + H

• Hypotenuse , H = 20 cm

➳ Per. = B + P + 20

• But it is given Per. = 48 cm , so ,

➳ 48 = B + P + 20

➳ B + P = 28

➳ P = 28 - B ... (1)

Area of a right triangle is ,

$\to \sf A=\dfrac{1}{2}\times b\times h$

where ,

• h denotes height = perpendicular (P)
• b denotes base = Base (B)

➠ A = ¹/₂ × B × P

• Given , Area of the triangle is 96 cm²

➠ 96 = ¹/₂ × B × P

➠ BP = 192

Sub. (1) ,

➠ B ( 28 - B ) = 192

➠ 28B - B² = 192

➠ B² - 28B + 192 = 0

➠ B² - 12B - 16B + 192 = 0

➠ B ( B - 12 ) - 16 ( B - 12 ) = 0

➠ ( B - 12 ) ( B - 16 ) = 0

➠ B = 12 ; 16 cm

Sub. B value in (1) ,

➠ P = 28 - (12)  or 28 - (16)

➠ P = 16 or 12

➠ P = 16 ; 12 cm

So ,

Base of the triangle = 12 or 16 cm  $\green{\bigstar}$

Perpendicular of the triangle = 16 or 12 cm  $\pink{\bigstar}$

Length of the perpendicular sides are 12 and 16 cm respectively