Answer:
P = 28 cm
Step-by-step explanation:
the diagonal divides the rectangle into 2 right triangles with the diagonal as hypotenuse.
the ratio of length : breadth = 4 : 3 = 4x : 3x ( x is a multiplier )
using Pythagoras' identity in the right triangle
(4x)² + (3x)² = 10²
16x² + 9x² = 100
25x² = 100 ( divide both sides by 25 )
x² = 4 ( take square root of both sides )
x =
= 2
then
length = 4x = 4 × 2 = 8 cm
breadth = 3x = 3 × 2 = 6 cm
perimeter (P) is calculated as
P = 2 × length + 2 × breadth
= 2 × 8 + 2 × 6
= 16 + 12
= 28 cm
Answer:
answer=14π
units=cm
Step-by-step explanation:
GIVEN
diameter (d) = 14 cm
radius (r) = d / 2 = 14 / 2 = 7
Now
Circumference (c)
= 2πr
= 2 * π * 7
= 14π cm
Answer: Choice B) {3, 5, sqrt(34)}
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Explanation:
We can only have a right triangle if and only if a^2+b^2 = c^2 is a true equation. The 'c' is the longest side, aka hypotenuse. The legs 'a' and 'b' can be in any order you want.
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For choice A,
a = 2
b = 3
c = sqrt(10)
So,
a^2+b^2 = 2^2+3^2 = 4+9 = 13
but
c^2 = (sqrt(10))^2 = 10
which is not equal to 13 from above. Cross choice A off the list.
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Checking choice B
a = 3
b = 5
c = sqrt(34)
Square each equation
a^2 = 3^2 = 9
b^2 = 5^2 = 25
c^2 = (sqrt(34))^2 = 34
We can see that
a^2+b^2 = 9+25 = 34
which is exactly equal to c^2 above. This confirms the answer.
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Let's check choice C
a = 5, b = 8, c = 12
a^2 = 25, b^2 = 64, c^2 = 144
So,
a^2+b^2 = c^2
25+64 = 144
89 = 144
which is a false equation allowing us to cross choice C off the list.