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Leona [35]
3 years ago
10

Look at the figure, PQRS. Find the values of x and y.

Mathematics
1 answer:
bekas [8.4K]3 years ago
4 0

Answer:

C. x = 5, y = 7

Step-by-step explanation:

Diagonals of a parallelogram bisects each other. Therefore:

2x = y + 3, and,

x + 2 = y

✔️To find the value of x, substitute y = (x + 2) in 2x = y + 3.

Thus:

2x = (x + 2) + 3

2x = x + 2 + 3

2x = x + 5

Subtract x from each side

2x - x = 5

x = 5

✔️To find y, substitute x = 5 in x + 2 = y.

Thus:

5 + 2 = y

7 = y

y = 7

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Here,
let width(b)be x then,
length (l)=9cm+x
area =112 sq cm
now,
area of rectangle=l*b
or, 112=(9+x)x
or, 112=9x+x^2
or, 0=x^2+9x-112
or, 0=x^2+(16-7)x-112
or, 0=x^2+16x-7x-112
or, 0=x(x+16)-7(x+16)
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either,
0=x-7
or,7=x
x=7cm
Or,
0=x+16
or, -16=x
x= -16[impossible,as distance is never negative] so,
x=7cm
therefore,length = 7cm + 9 cm = 16cm and width = 7cm.
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