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High School Math : How to find the length of the side of a 45/45/90 right isosceles triangle

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Example Question #442 : Geometry

What is the area of a square that has a diagonal whose endpoints in the coordinate plane are located at (-8, 6) and (2, -4)?

Possible Answers:

100

50√2

200√2

100√2

Correct answer:

100

Explanation:

Square_part1

Square_part2

Square_part3

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Example Question #1 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle

Isosceles

An isosceles triangle has a hypotenuse of h=7in $\displaystyle h=7in$. Find the length of its sides, $\displaystyle x$.

Possible Answers:

Not enough information to solve

4.95in $\displaystyle 4.95in$

2.64in $\displaystyle 2.64in$

7in $\displaystyle 7in$

5.94in $\displaystyle 5.94in$

Correct answer:

4.95in $\displaystyle 4.95in$

Explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as $45^{\circ}-45^{\circ}-90^{\circ}$ $\displaystyle 45^{\circ}-45^{\circ}-90^{\circ}$ triangles and their side lengths follow a specific pattern that states you can calculate the length of the legs of an isoceles triangle by dividing the length of the hypotenuse by the square root of 2

$x=\frac{h}{\sqrt{2}}$ $\displaystyle x=\frac{h}{\sqrt{2}}$

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

$\rightarrow 4.95in$ $\displaystyle \rightarrow 4.95in$

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Example Question #2 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle

Isosceles

The measure of the sides of this isosceles right triangle are $x=3\sqrt{2}$ $\displaystyle x=3\sqrt{2}$. Find the measure of its hypotenuse, $\displaystyle h$.

Possible Answers:

$\displaystyle 7$

$\displaystyle 8$

$\displaystyle 18$

$\displaystyle 6$

Not enough information to solve

Correct answer:

$\displaystyle 6$

Explanation:

An isosceles triangle is a special triangle due to the values of its angles. These triangles are referred to as $45^{\circ}-45^{\circ}-90^{\circ}$ $\displaystyle 45^{\circ}-45^{\circ}-90^{\circ}$ triangles and their side lenghts follow a specific pattern that states you can calculate the length of the hypotenuse of an isoceles triangle by multiplying the length of one of the legs by the square root of 2.

$h=x\sqrt{2}$ $\displaystyle h=x\sqrt{2}$

$h=3\sqrt{2}*\sqrt{2}$ $\displaystyle h=3\sqrt{2}*\sqrt{2}$

h=3*2 $\displaystyle h=3*2$

$\rightarrow6$ $\displaystyle \rightarrow6$

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High School Math : How to find the length of the side of a 45/45/90 right isosceles triangle

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #442 : Geometry

Example Question #1 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle

Example Question #2 : How To Find The Length Of The Side Of A 45/45/90 Right Isosceles Triangle

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