Answer:

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→A=

2

1

×b×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