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Answers
Answer:
8. Let the number be x
According to the question
8x−10=6x+4
8x−6x=10+4
2x=14
x=7
Therefore the number is 7
9. -7/8
10. x+y=58 (i)
x=58-y (ii)
x-y=28. (iii)
Substitute value of x in equation iii
58-y-y = 28
58-2y = 28
58-28 = -2y
30/(-2) = y
y = -15
Substitute value of y in equation ii
x-(-15) = 28
x+15 = 28
x = 28-15
x = 13
11. Proof: In the quadrilateral ABCD,
∠ABC, ∠BCD, ∠CDA, and ∠DAB are the internal angles.
AC is a diagonal
AC divides the quadrilateral into two triangles, ∆ABC and ∆ADC
We have learned that the sum of internal angles of a quadrilateral is 360°, that is, ∠ABC + ∠BCD + ∠CDA + ∠DAB = 360°.
let’s prove that the sum of all the four angles of a quadrilateral is 360 degrees.
We know that the sum of angles in a triangle is 180°.
Now consider triangle ADC,
∠D + ∠DAC + ∠DCA = 180° (Sum of angles in a triangle)
Now consider triangle ABC,
∠B + ∠BAC + ∠BCA = 180° (Sum of angles in a triangle)
On adding both the equations obtained above we have,
(∠D + ∠DAC + ∠DCA) + (∠B + ∠BAC + ∠BCA) = 180° + 180°
∠D + (∠DAC + ∠BAC) + (∠BCA + ∠DCA) + ∠B = 360°
We see that (∠DAC + ∠BAC) = ∠DAB and (∠BCA + ∠DCA) = ∠BCD.
Replacing them we have,
∠D + ∠DAB + ∠BCD + ∠B = 360°
That is,
∠D + ∠A + ∠C + ∠B = 360°.
Or, the sum of angles of a quadrilateral is 360°. This is the angle sum property of quadrilaterals.
12. 17/24
13. (2/5)³×(25/4)² = (8/125)(625/16)
= 5000/2000
= 5/2
14. perimeter of rectangular park = 400 m
let breadth be x
therefore,
2(l+b) = 400
2(26+b+b) = 400
(26+b+b) = 400/2
(26+b+b) = 200
2b = 200-26
2b = 174
b = 174/2
b = 87
therefore, breadth = 84m and length = 84+26m = 110 m
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