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A wall in Maria's bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle.

Using the [tex]$45^{\circ}-45^{\circ}-90^{\circ}$[/tex] triangle theorem, find the value of [tex]$h$[/tex], the height of the wall.

A. 6.5 ft

B. [tex]$6.5 \sqrt{2}$[/tex] ft

C. 13 ft

D. [tex]$13 \sqrt{2}$[/tex] ft


Sagot :

Sure, let's find the height [tex]\( h \)[/tex] of the wall using the properties of a [tex]\( 45^{\circ}-45^{\circ}-90^{\circ} \)[/tex] triangle.

A [tex]\( 45^{\circ}-45^{\circ}-90^{\circ} \)[/tex] triangle is a special type of right triangle where the two legs are equal in length, and the hypotenuse is [tex]\( \sqrt{2} \)[/tex] times the length of each leg.

Given:
- One of the legs of the triangle (which we'll call [tex]\( a \)[/tex]) is [tex]\( 6.5 \)[/tex] feet.

We need to find the height [tex]\( h \)[/tex], which corresponds to the hypotenuse of the triangle.

According to the properties of a [tex]\( 45^{\circ}-45^{\circ}-90^{\circ} \)[/tex] triangle:

[tex]\[ h = a \sqrt{2} \][/tex]

Substitute [tex]\( a = 6.5 \)[/tex] feet into the equation:

[tex]\[ h = 6.5 \times \sqrt{2} \][/tex]

By multiplying these values together, we get:

[tex]\[ h \approx 9.19238815542512 \][/tex]

Therefore, the height of the wall, [tex]\( h \)[/tex], is approximately [tex]\( 9.19238815542512 \)[/tex] feet.