Question

the hypotenuse of a Right triangle is 4√5cm.if the smaller side is tripled and the larger side is doubled , the new hypotenuse will be 20cm .find the length of each side.​

Answer 1

Answer:

4, 8, 4√5

Step-by-step explanation:

We can use the Pythagorean Theorem for this

$a^2+b^2 = (4\sqrt{5})^2\\=a^2+b^2 = 80$

We can also write

$(3a)^2+(2b)^2=20^2\\= 9a^2+4b^2 = 400$

We can multiply the first equation by 4 to get

$4a^2+4b^2=320$

Subtracting the first equation from the second we get

$5a^2=80\\a^2 = 16\\a=4$

Solving for b we get

b = 8

Thus our sides are 4, 8, 4√5