Question

question 23 of 28 what is the length of each leg in the right triangle shown? a. 7 b. $sqrt{2}$ c. 2 d. $7sqrt{2}$

Explanation:

Step1: Recall 45 - 45 - 90 triangle ratio

In a 45 - 45 - 90 right - triangle, the ratio of the sides is $1:1:\sqrt{2}$. Let the length of each leg be $x$. Then the hypotenuse $c$ is related to the leg length $x$ by $c = x\sqrt{2}$.

Step2: Set up an equation

We are given that the hypotenuse $c = 7\sqrt{2}$. Since $c=x\sqrt{2}$, we have the equation $x\sqrt{2}=7\sqrt{2}$.

Step3: Solve for $x$

Divide both sides of the equation $x\sqrt{2}=7\sqrt{2}$ by $\sqrt{2}$. So, $x = 7$.

Answer:

A. 7