A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #8 #, #7 #, and #14 #, respectively. What is the rectangle's area?

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Answer 1 · 2016-10-30T05:39:08

#54.18#

Draw the diagram

enter image source here

To find the are of the triangle at the bottom,

We need to find the length of #"B"#

As the triangle is a right angle triangle,

We use the #color(blue)("Pythagoras theorem"#

#color(blue)(a^2+b^2=c^2#

Where,

#color(orange)("c = Longest side (hypotenuse)"#

#color(orange)("a and b are the other sides"#

So,

#color(purple)(c=8#

#color(purple)(b="B"#

#color(purple)(a=7#

Insert the following (above) in the formula

#rarr7^2+"B"^2=8^2#

#rarr49+"B"^2=64#

#rarr"B"^2=64-49#

#rarr"B"^2=15#

Take the square root of both sides

#rarrsqrt("B"^2)=sqrt(15)#

#color(green)(rArr"B"=sqrt15~~3.87#

Let's redraw the diagram

enter image source here

Now, we need to find the area of the rectangle

We use the formula

#color(brown)("Area of rectangle"=l*b#

Where,

#color(orange)(l="length"=14#

#color(orange)(b="breadth"=sqrt15#

#rarrl*b#

#rarr14*sqrt15#

#rarr14sqrt15#

#rarr14*3.87#

#color(green)(rArr54.18#