Question

Help please ive tried with my friends and no luck

Answer 1

Answer:

$a=5 \sqrt{7}$

Step-by-step explanation:

Pythagoras Theorem explains the relationship between the three sides of a right triangle.  The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle:

    $a^2+b^2=c^2$

where:

• a and b are the legs of the right triangle
• c is the hypotenuse (longest side) of the right triangle

Given:

• b = 9
• c = 16

Substitute the given values into the formula and solve for a:

$\begin{aligned}a^2+b^2 & = c^2 \\\implies a^2+9^2 & =16^2\\a^2+81 & =256\\a^2+81-81 & =256-81\\a^2 & =175\\\sqrt{a^2} & =\sqrt{175}\\a & =\sqrt{25 \cdot 7}\\& = \sqrt{25}\sqrt{7}\\& =5\sqrt{7}\end{aligned}$

Therefore, the measure of the third side of the given right triangle is $5 \sqrt{7}$

Learn more about Pythagoras Theorem here:

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