Question

How do you find the hypotenuse if the length of the legs of a right triangle are $30ft$ and $40ft$ ?

Answer 1

Hint: In this question, we have to find the hypotenuse of the right angle triangle. Thus, we will use the hypotenuse formula to get the solution. Also, the other two sides of the triangle given to us are $30ft$ and $40ft$ . Therefore, we will apply the formula ${{\left( \text{hyotenuse} \right)}^{2}}\text{=}{{\left( \text{other side} \right)}^{2}}\text{+}{{\left( \text{base} \right)}^{2}}$ . Thus, in this case we will say the base is equal to $30ft$ and the other side of the triangle is equal to $40ft$ . Therefore, we will substitute these values in the formula, after that we will open the brackets and then make the necessary calculations. In the end, we will take the square root on both sides of the equation, to get the required solution for the problem.

Complete step by step solution:
According to the problem, we have to find the value of hypotenuse of a triangle.
Thus, we will use the hypotenuse formula ${{\left( \text{hypotenuse} \right)}^{2}}\text{=}{{\left( \text{other side} \right)}^{2}}\text{+}{{\left( \text{base} \right)}^{2}}$ ------ (1) to get the solution.
Now, we know that the length of two sides given to us is $30ft$ and $40ft$ . Thus, let us suppose the other side of the triangle is equal to $40ft$ and base of the triangle is equal to $30ft$. So, we will substitute these values in equation (1), we get
$\Rightarrow {{\left( \text{hypotenuse} \right)}^{2}}={{\left( 40 \right)}^{2}}+{{\left( 30 \right)}^{2}}$
Now, we will open the brackets of the above equation, we get
$\Rightarrow {{\left( \text{hypotenuse} \right)}^{2}}=1600+900$
$\Rightarrow {{\left( \text{hypotenuse} \right)}^{2}}=2500$
Now, we will take the square root on both sides of the equation, we get
\[\Rightarrow \sqrt{{{\left( \text{hypotenuse} \right)}^{2}}}=\sqrt{2500}\]
On further solving the above equation, we get
$\Rightarrow \text{hypotenuse}=\pm 50ft$
Now, we know that the side of the triangle cannot be negative, thus we ignored that value.
Therefore, the value of hypotenuse of the triangle, if the length of the legs of a right triangle are $30ft$ and $40ft$ is equal $50ft$ .

Note: While solving this problem, do mention all the steps properly to avoid confusion and mathematical error. Do not forget to mention the standard unit in the last to get an accurate solution. Also, when we take the square root, always mention the $\pm $ sign.