 # The legs of a right triangle are 6 and 8 cm. Find the hypotenuse and the area of ​​the triangle. calcific5z 2022-09-12 Answered
The legs of a right triangle are 6 and 8 cm. Find the hypotenuse and the area of ​​the triangle.
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a=6 cm
b=8 cm
c - ? cm
S-? $c{m}^{2}$
Solution:
according to the Pythagorean theorem: ${a}^{2}+{b}^{2}={c}^{2}$
where a, b - legs, c - hypotenuse
$c=\sqrt{{a}^{2}+{b}^{2}}=\sqrt{{6}^{2}+{8}^{2}}=\sqrt{36+64}=\sqrt{100}=10\left(cm\right)$- hypotenuse $\mathrm{△}$
$S=\frac{1}{2}ab=\frac{1}{2}\ast 6\ast 8=24\left(c{m}^{2}\right)$
Answer: 10cm hypotenuse $\mathrm{△}$ ; $24c{m}^{2}$ square $\mathrm{△}$

We have step-by-step solutions for your answer! Teagan Sutton
According to the Pythagorean theorem, the square of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the legs (a and b), ${c}^{2}={a}^{2}+{b}^{2}$.
${c}^{2}={6}^{2}+{8}^{2}$
${c}^{2}=100$
c=10 cm.
The hypotenuse is 10 cm.
The area of ​​a triangle is half the product of its legs.
S=0.5*ab
S=0.5*8*6.
$S=24c{m}^{2}$.
The area of ​​a triangle is $24c{m}^{2}$.
Answer: $10cm,24c{m}^{2}$.

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