1. A number is twice the other number. When the larger is subtracted from 50, the result is 2 more than when the smaller is subtracted from 40. Find the numbers. 4 marks 2. The length of a rectangle exceeds twice its width by 3. Find the length and breadth of the rectangle if it's perimeter is 246 m. 3 marks 3. The measure of adjacent angles of a parallelogram are in the radio 2:7. Find all the angles of parallelogram. 3 marks.
Answers
Answer:
Given =A number is twice another number.
1.Let the smaller number be x and
Let the larger number be 2x.
Now , A.T.Q.
50 - 2x = 40 - x + 2
-2x + x = 42 - 50
- x = -8
x = 8
Hence the smaller number is 8
Now for bigger number 2x= 2(8) = 16
2.Length of the Rectangle = exceeds twice its breadth by 2 cm
3.Given:-
Perimeter = 246 m
Length is 3 metre more than 2x its breadth.
Solution
Let us assume breadth as x.
So, length is 3+2x
According to the question:-
Perimeter = 2(L+B)
L is length
B is breadth
=246=2(3+2x+x)
=246=2(3+3x)
=246=6+6x
=246-6=6x
=240=6x
x=240÷6
x=80m
4.Let two adjacent angles A and B of ∥gm ABCD be 3x and 2x respectively.
Since the adjacent angles of a parallelogram are supplementary.
∠A+∠B=180
o
⇒3x+2x=180
o
⇒5x=180
o
⇒x=
5
180
o
=36
o
∴∠3×36
o
=108
o
and, ∠B=2×36
o
=72
o
Since the opposite angles are equal in a parallelgram, therefore, ∠C=∠A=108
o
and ∠D=∠B=72
o
Hence, ∠A=108
o
,∠B=72
o
,∠C=108
o
and ∠D=72
o
Step-by-step explanation:
1.
Given =A number is twice another number.
Let the smaller number be x and
Let the larger number be 2x.
Now, A.T.Q.
50 - 2x = 40 - x + 2
-2x + x = 42 - 50
- x = -8
x = 8
Hence the smaller number is 8
Now for bigger number 2x = 2(8) = 16
2.
Let breadth be equal to x
then length= 2x + 3
perimeter of rectangle= 2(l + b)
= 4x + 6 +2x
=6x + 6
we know the perimeter
so it would be
246 = 6x + 6
240 = 6x
x = 240/6
x = 40m
Breadth = 40m
Length = 80 + 3 = 83m
3.
let the ratio be x
1st angle = 2x
2nd angle = 7x
we know that sum of two adjacent angles of parallelogram =180
7x + 2x = 180
9x = 180
x = 20
so...
1st angle = 2x = 2 × 20 = 40
2nd angle = 7x = 7 × 20 = 140
Mark answer as the brainliest.