Question

the ratio of the sides of a right triangle is 7:12:13. if the area of the triangle is 3024cm^2 what is the length of the hypotenuse

Answer 1

Answer:

Length of hypotenuse

is 78√2 cm .

Step-by-step explanation:

Let the sides of ∆ be 7x , 12x , 13x

Since , Hypotenuse is the longest side of any ∆

therefore, length of hypotenuse be 13x

let the length of base be 7x

and the length of height be 12x

A/q

Area of ∆ = 3024 cm^2

=> 1/2 × base × height = 3024

=>1/2 × base × height = 3024

=> base × height = 3024 × 2

=> 7x × 12x = 6048

=> 84 x^2 = 6048

=> x^2 = 6048/84

=> x^2 = 72

=> x = √72

=> x = √2×6×6

=> x = 6 √2

Now ,

Length of Hypotenuse = 13x

= 13 × 6 √2

= 78 √2 cm

Hence , the length of hypotenuse

is 78√2 cm.