Given: a = 8 cm;
c = 10 cm;
Find: Spr -? cm ^ 2.
This rectangle is divided by the diagonal in half into two equal right-angled triangles with legs a, b and hypotenuse c.
Consider one of these triangles:
By the Pythagorean theorem, c ^ 2 = a ^ 2 + b ^ 2, hence b ^ 2 = c ^ 2 – a ^ 2.
Thus, b = sqrt (c ^ 2 – a ^ 2) = sqrt (10 ^ 2 – 8 ^ 2) = sqrt (36) = ± 6, namely, b = 6 cm, since the length value can only be positive.
The area of the rectangle is found by the formula:
Sp. = a * b = 8 * 6 = 48 (cm ^ 2).
Answer: Sp. = 48 cm ^ 2.
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