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 15, 1 1, and 4 4, respectively. What is the rectangle's area?

1 Answer
Jim G.
Mar 20, 2016

≈ 59.87 square units

Explanation:

The area of the rectangle = 4B . To calculate the value , requires knowing the value of B.
Since the triangle is right we can find B, usingcolor(blue)" Pythagoras' theorem " Pythagoras' theorem

The hypotenuse is A hence : A^2 = B^2 + C^2 A2=B2+C2

and B^2 = A^2 -C^2 = 15^2 - 1^2 = 224 B2=A2−C2=152−12=224

now B^2 = 224 rArr B = sqrt224 B2=224⇒B=√224

and area of rectangle = 4B = 4xxsqrt224 ≈ 59.874×√224≈59.87

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