# A 45-45-90 triangle has a hypotenuse of length 7. What is the length of one of its legs?

May 11, 2018

$\frac{7 \sqrt{2}}{2}$

#### Explanation:

In a $45 - 45 - 90$ triangle the two shorter sides are equal since it is also an isosceles triangle. Using Pythagoras' theorem

${x}^{2} + {x}^{2} = {7}^{2}$

$2 {x}^{2} = 49$

x=sqrt(49/2

$x = \frac{7}{\sqrt{2}} = \frac{7 \sqrt{2}}{2}$

May 11, 2018

color(indigo)("Length of each leg " a = 7 / sqrt2 = 4.95

#### Explanation:

"From the above figure, sides are in the ratio ' a : a : asqrt2

$\text{Given hypotenuse } = a \sqrt{2} = 7$

$\therefore a = \frac{7}{\sqrt{2}} = \frac{7}{1.4142} = 4.95$