Question

Which equations are correct for the right triangle shown ?

$\begin{array}{l}\left(a\right).r^2=s^2+t^2\left(b\right).{\text{s}}^2=r^2+t^2\left(c\right).{\text{s}}^2+r^2=t^2\\ \left(d\right).s^2=t^2-r^2\left(e\right).t=r+s\left(f\right).t^2={\left(r+s\right)}^2\end{array}$

Short answer

The correct equation is,

$t^2=r^2+s^2$

Step-by-step solution

Step 1. Given information.

We have given a figure as shown below.

Step 2. Use Pythagorean Theorem.

From Pythagorean Theorem we know that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

Step 3. The given triangle is right triangle.

Therefore,

$t^2=r^2+s^2$

It can also be written as,

$s^2=t^2-r^2$

Therefore, the correct equation is option $\left(d\right).$