Figure LMNO is a parallelogram. What is the value of x?
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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