Question

11. The lengths of two sides of a right triangle containing the right angle differ by 2 cm. If the
triangle whose height is 12 cm. Write your
to two decimal places.
area of the triangle is 24 cm”, find the perimeter of the triangle.
​

Answer 1

Step-by-step explanation:

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Let one side be = x i.e base

then other side will be y i.e height

Their difference is 2

x - y = 2

y = x - 2.....

Area = ½ × b × h = 24

½ × x × ( x - 2 ) = 24

x² - 2x - 48 = 0

x² - 8x + 6x - 48 = 0

x × ( x - 8 ) + 6 × ( x - 8 ) = 0

( x + 6 ) × ( x - 8 ) = 0

x = - 6 or 8 cm

side cannot be in negative.... so x = 8 cm

y = x - 2 = 6 cm

Hypotenuse = √ ( 8² + 6² )

= √ ( 100 )

= 10 cm

So perimeter is.....

Perimeter = x + y + hypotenuse

= 8 + 6 + 10

= 24 cm......