Solve {l}{a=60}{b=245}{c=sqrt{a^2+b^2}}{text{Solvefor}dtext{where}}{d=c}

$$\left. \begin{array} { l } { a = 60 }\\ { b = 245 }\\ { c = \sqrt{a ^ {2} + b ^ {2}} }\\ { \text{Solve for } d \text{ where} } \\ { d = c } \end{array} \right.$$

Solve for a, b, c, d

$$d=5\sqrt{2545}\approx 252.239965113$$

Solution Steps

Consider the third equation. Insert the known values of variables into the equation.

$$c=\sqrt{60^{2}+245^{2}}$$

Calculate 60 to the power of 2 and get 3600.

$$c=\sqrt{3600+245^{2}}$$

Calculate 245 to the power of 2 and get 60025.

$$c=\sqrt{3600+60025}$$

Add 3600 and 60025 to get 63625.

$$c=\sqrt{63625}$$

Factor 63625=5^{2}\times 2545. Rewrite the square root of the product \sqrt{5^{2}\times 2545} as the product of square roots \sqrt{5^{2}}\sqrt{2545}. Take the square root of 5^{2}.

$$c=5\sqrt{2545}$$

Consider the fourth equation. Insert the known values of variables into the equation.

$$d=5\sqrt{2545}$$

The system is now solved.

$$a=60 b=245 c=5\sqrt{2545} d=5\sqrt{2545}$$