Practice! #2

Algebra Level 3

Given that, $a^{2}+b^{2}=c^{2}$ , $a+b+c=22$ , $ab=21$ ,and $a,b,c$ is real number. What is the value of $c^{2}$ ?

Give your answer up to 2 decimal places

The answer is 100.91.

1 solution

Fidel Simanjuntak
Mar 10, 2017

$\begin{aligned} a+b+c & = 22 \\ a+b & = 22-c \quad \Rightarrow \color{#3D99F6} \text{Squaring both sides} \\ \color{#D61F06} a^{2} \color{#333333} + 2ab + \color{#D61F06} b^{2} & \color{#333333} = 484 - 44c + c^{2} \quad \Rightarrow \color{#D61F06} \text{Note that } a^{2} + b^{2} = c^{2} \\ \color{#333333} \cancel{c^{2} } + 2(21) & = 484 -44c + \cancel{c^{2} } \\ 42 & = 484 - 44c \\ c & = \dfrac{442}{44} \\ c^{2} & = \dfrac{442^2}{44^2} \approx \boxed{\color{#D61F06} 100.91} \end{aligned}$

Practice! #2

The answer is 100.91.

1 solution

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