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 #15/8 #, #3/5 #, and #7 #, respectively. What is the rectangle's area?

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Answer 1 · 2017-12-03T13:32:57

The area of the rectangle is 12.46 square units

The area of the rectangle is the product of the lengths of two sides.

One side is given as 7; the other side is B, the length of one leg of the right triangle.

So Area equals 7 times B
#A = 7 xx B#

First find B

The Pythagorean Theorem for this triangle is
#A^2 = B^2 + C^2#
where A is the hypotenuse and C is one of the legs

Sub in the numerical values and solve for B.

. . #A^2 . . = B ^2 + . .C ^2#
#((15)/(8))^2 = B ^2 + ((3)/(5))^2#

1) Clear the parentheses by squaring the fractions

#(225) / (64) = B ^2 + (9)/(25)#

2) Subtract # (9)/(25)# from both sides to isolate #B ^2#

#(225) / (64) - (9)/25 = B ^2#

3) Give the fractions a common denominator

#(225*25 - 9*64) / (64*25) = B ^2#

#(5625 - 576) / (1600) = B ^2#

#(5049)/(1600) = B ^2#

#3.156 = B ^2#

4) Find the square roots of both sides

#1.78 = B#
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Now you can find the Area.

It is B #xx 7#

#7 xx 1.78 = 12.46# #larr# answer

Answer:
The area of the rectangle is 12.46 square units