Question

the area of a right angled triangle is 24sq.cm and length of hypotenuse is 10cm. find length of shortest leg​

Answer 1

Answer:

≈ 6 cm

Step-by-step explanation:

Given :

Hypotenuse ( c ) = 10 cm

Area ( A ) = 24 cm²

Formulas Using :

1 ] A = ab

       2

2 ] c = √a² + b²

There are 2 solutions for a :

a = √2. c²√c²+√c⁴- 16.A² - √2.√c⁴ - 16. A² √c²+√c⁴ - 16.A²

                                        8A

a = √2 .10².√10²+√10⁴- 16.24² - √2.√10⁴ - 16. 24² √10²+√10⁴ - 16.24²

                                          8 x 24

≈ 6 cm

a = √2. c²√c²+√c⁴- 16.A² + √2.√c⁴ - 16. A² √c²+√c⁴ - 16.A²

                                        8A

a = √2 .10².√10²+√10⁴- 16.24² + √2.√10⁴ - 16. 24² √10²+√10⁴ - 16.24²

                                          8 x 24

= 8 cm

Since ' ≈ 6 ' is smaller than 8 , the length of the shortest leg ( a ) would be

approximately 6 cm or simply ' ≈ 6 '

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