Question

do these measurements form a right triangle?
side 1: $5\sqrt{113}$
side 2: 40
side 3: 35

show your work here
hint: to add the square root symbol ($\sqrt{\square}$), type
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Explanation:

Step1: Identify longest side

Longest side is $5\sqrt{113}$, so test if $(5\sqrt{113})^2 = 40^2 + 35^2$.

Step2: Calculate left-hand side

$$(5\sqrt{113})^2 = 5^2 \times (\sqrt{113})^2 = 25 \times 113 = 2825$$

Step3: Calculate right-hand side

$$40^2 + 35^2 = 1600 + 1225 = 2825$$

Step4: Compare both sides

Left-hand side = Right-hand side, so Pythagorean theorem holds.

Answer:

Yes, these measurements form a right triangle.