Question

If \[{r^2} = {l^2} + {d^2}\] Solve for d, and find the value of d if r=5 and l=4.

Answer 1

Hint:
We are given the formula or equation we can say in question. But it gives the value of \[{r^2}\]. Students we will rearrange the terms to get the equation that will give us the value of d. Then putting the values of r and l we will get the value of d. Let’s solve it!

Complete step by step solution:
We are given that
\[{r^2} = {l^2} + {d^2}\]
Rearranging the terms,
\[{r^2} - {l^2} = {d^2}\]
Now on taking square root on both sides,
\[\sqrt {{r^2} - {l^2}} = d\]
Let’s take unknown on LHS
\[ \Rightarrow d = \sqrt {{r^2} - {l^2}} \]
Now this is the formula or rearranged equation for d. now putting the values of r and l that are given,
\[ \Rightarrow d = \sqrt {{5^2} - {4^2}} \]
Performing the squares,
\[ \Rightarrow d = \sqrt {25 - 16} \]
Subtract the terms
\[ \Rightarrow d = \sqrt 9 \]
Taking the root
\[ \Rightarrow d = 3\]
Hence the value of d is 3.

Note:
Here in this problem we may mistakenly find the value of \[{d^2}\] , but we are asked to find the value of d. We also can use \[{a^2} - {b^2} = \left( {a - b} \right)\left( {a + b} \right)\] to solve the problem.