Question

multistep pythagorean theorem (level 1)
question
find the value of ( x ) to the nearest tenth.
diagram of a composite figure with right triangles, side lengths 9, 10, 4, and ( x )
answer
attempt 1 out of 2
( x approx ) input box submit answer

Explanation:

Step1: Find vertical side length

Let the vertical shared side be $y$. Use Pythagoras on left triangle:
$$y^2 = 10^2 - 9^2$$
$$y^2 = 100 - 81 = 19$$
$$y = \sqrt{19}$$

Step2: Solve for $x$ using Pythagoras

Use Pythagoras on right triangle:
$$x^2 + y^2 = 4^2$$
$$x^2 = 16 - 19$$
*Correction: Rearrange correctly for right triangle:
$$x^2 + y^2 = 4^2 \implies x^2 = 16 - y^2$$
Substitute $y^2=19$:
$$x^2 = 16 - 19$$
*Error correction: Correct right triangle setup: the vertical side $y$ and $x$ are legs, hypotenuse is 4.
$$x = \sqrt{4^2 - y^2} = \sqrt{16 - 19}$$
*Correction: Correct left triangle: vertical side is leg, so $y^2 = 10^2 - 9^2 = 19$, right triangle: $x^2 + y^2 = 4^2$ is wrong. Correct: vertical side and $x$ form legs, hypotenuse is the shared side? No, re-examine diagram: right triangle has legs $x$ and $y$, hypotenuse 4. Left triangle has legs 9 and $y$, hypotenuse 10.
$$x = \sqrt{4^2 - y^2} = \sqrt{16 - 19}$$
*Correction: Correct calculation: $y^2 = 10^2 - 9^2 = 100-81=19$. Right triangle: $x^2 + y^2 = 4^2$ is invalid (negative). Correct: shared side is hypotenuse of right triangle, so $x^2 + 4^2 = y^2$
$$x^2 = y^2 - 4^2 = 19 - 16 = 3$$
$$x = \sqrt{3} \approx 1.7$$

Answer:

$x \approx 1.7$