Nautical flags are used to represent letters of alphabets. the flag for the letter o consists of a yellow right triangle and a red right triangle joined together along their hypotenuse to form a square. the joint hypotenuse of the two triangles is three inches longer than a side of the square. find the length of a side of the flag. round your answer to the nearest tenth.

The length of a side of the flag is 7.2inches

Step-by-step explanation:

Let length = x

Let hypotenuse = x+3

Using Pythagoras' Theorem:

x^2 + x^2 = (x+3)^2

x^2 + x^2 = x^2 + 6x + 9

2x^2 = x^2 + 6x + 9

×^2 - 6x - 9 = 0

x=[-(-6)+sqrt.(-6)^2-4(1)(-9)]/2(1)

×=[6+sqrt.72]/2

×=7.2inches

×=[-(-6)+sqrt.(-6)^2-4(1)(-9)]/2(1)

x=[6-sqrt.72]/2

×=-1.2(rej)

(PS. sqrt is square root)

(Correct me if i am wrong)

7.2 in

Step-by-step explanation:

Let length of side of flag=x

Hypotenuse of right triangle=x+3

According to question information

Using Pythagoras theorem

Using identity:

Using quadratic formula :

It is not possible because the length of side is always positive.

Hence, the side of flag=7.2 in

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step-by-step explanation: