Answer:
see explanation
Step-by-step explanation:
(10)
(a)
The opposite sides of the rectangle are equal, then perimeter P is
P = 2(4p - 6) + 2(p + 13) ← distribute parenthesis and simplify
= 8p - 12 + 2p + 26
= 10p + 14
Given P = 84 , then
10p + 14 = 84 ( subtract 14 from both sides )
10p = 70 ( divide both sides by 10 )
p = 7
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(b)
The area (A) of the shaded region is calculated as
A = area of rectangle - area of triangle
area of rectangle = (4p - 6)(p + 13) ← expand using FOIL
= 4p² + 46p - 78 ← substitute p = 7
= 4(7)² + 46(7) - 78
= 4(49) + 322 - 78
= 196 + 244
= 440 cm²
area of triangle = [tex]\frac{1}{2}[/tex] bh
= [tex]\frac{1}{2}[/tex]( 3p - 3)( p + 13) ← substitute p = 7
= [tex]\frac{1}{2}[/tex](3(7) - 3)(7 + 13)
= [tex]\frac{1}{2}[/tex](21 - 3)(20)
= [tex]\frac{1}{2}[/tex] × 18 × 20 = 9 × 20 = 180 cm²
Then
A = 440 - 180 = 260 cm²
(11)
pole B = [tex]\frac{1}{2}[/tex] × 72 = 36
pole A = [tex]\frac{5}{6}[/tex] × 36 = 5 × 6 = 30 m
