12 mm 9 mm What is the length of the hypotenuse?

Mathematics

1 answer:

stepan [7]3 years ago

5 0

Step-by-step explanation:

By Pythagoras's theorem,

hypotenuse^2 = 12^2 + 9^2

hypotenuse = ±15mm (rej -15mm since hypotenuse > 0mm)

therefore, 15mm

Topic: Pythagoras theorem

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Sedaia [141]

Answer:

$\huge\boxed{\sf Volume = 384 \ cm^3}$

Step-by-step explanation:

Slant Height = 10 cm

Base Edge = 12 cm

<u>Finding the Height using Pythagorean Theorem:</u>

$\sf c^2 = a^2 + b^2 \\\\Where \ c = 10\ cm , b = 6\ cm [Half of 12] \ and \ a \ is \ height\\\\10^2 = a^2 + 6^2\\\\100=a^2 +36\\\\100-36 = a^2\\\\64 = a^2\\\\Taking \ sqrt \ on \ both \ sides\\\\Height= 8 \ cm$

$\rule[225]{225}{2}$

<u>Now, Finding the volume:</u>

$\sf Volume = a^2 \frac{h}{3}\\\\ Where \ a \ is base \ edge \ and \ h \ is \ height\\\\Volume = (12)^2 \frac{8}{3} \\\\Volume = 144 \frac{8}{3} \\\\Volume = 48*8\\\\\bold{Volume = 384 \ c m^3}$