Question

The area of a right angle triangle is 30 cm square and the length of its hypotenuse is 13 cm. The length of the shorter leg is

Answer 1

hey buddy ,

area of triangle = 1/2 × base × height

=> 30 cm² = 1/2 × base × height

=> 60 cm² = base × height
(equation 1)
=> height = 60/base
=> h = 60/b

=> multiply each side of equation 1 by 2 ,
we get ,

=> 120 cm² = 2bh (b :- base & h :- height) (equation 2)

(hypotenuse)² = base ² + height ²

=> 13² = base ² + height ²

=> 169 = b²+h² (equation 3)

adding equation 2 and 3

=> 289 = b²+h²+2bh

=> 289 cm² = (b+h)²

=> √289 cm² = 17 cm = (b+h)

=> substitute value of h in this equation ,

=> 17 cm = b + 60/b

=> 17 = (b²+60)/b

=> 17b = b²+60

=> b²+60-17b = 0

=> b²-17b+60 = 0

by splitting the middle term,

=> b²-5b-12b+60 = 0

=> b(b-5) - 12(b-5) = 0

=> (b-5) (b-12) = 0

if , b-5 = 0

=> b = 5 cm

or , if b-12 = 0

=> b = 12 cm

if base = 5cm
then , height is 12 cm

and base is shorter leg

and if base = 12 cm

then , height is 5 cm

and height is shorter leg

hope this helps
any confusion then ask in comments or inbox

Answer 2

Step-by-step explanation:

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