Areas

If the height of a triangle is decreased by 40% and its base is increased by 40% what will be the effect on its area?

by
If the height of a triangle is decreased by 40% and its base is increased by 40% what will be the effect on its area?

A. No change
B. 8%decrease
C. 16% Decrease
D. 16%increases

Explanation:
let the height be ‘h’ and base = b, then area =(1/2 bh)sq.units
New height =(60 % of h) = (60/100 h) = 3h/5
New base =(140% of b) =(140/100 b) =(76/5)
New area =(1/2 x 7b/5 x 3h/5) Sq.units =(21/50 bh)sq.units
Decrease in area =(1/2bh – 21/50bh)= 4/50 bh
Decrease % =(4/50bh. 2/bh x 100)% =16%

The sides of a triangle are in the ratio ½: 1/3: ¼. If the perimeter is 52cm then the length of the smallest side is________?

by
The sides of a triangle are in the ratio ½: 1/3: ¼. If the perimeter is 52cm then the length of the smallest side is________?

A. 9cm
B. 10cm
C. 11cm
D. 12cm
Explanation:
Ratio of sides = ½ : 1/3 : ¼ = 6: 4 : 3
Side are (32 x 6/13)cm, (32 x 4/13)cm and (52 x 3/13)cm i.e…, 24 cm , 16 cm, 12 cm.
Length of smallest side = 12 cm

If each side of a square is increased by 50% the ratio of the area of the resulting square to the area of the given square is__________?

by
If each side of a square is increased by 50% the ratio of the area of the resulting square to the area of the given square is__________?

A. 5:4
B. 9:4
C. 4:5
D. 4:9

Explanation:
Let original side be x metres, then area = x2 Sq.m
New side =(150% of x)m = (150/100 × x)m =(3x/2)m
New area =(3x/2 x 3x/2)m2 = 9×2/4 m2
Required ratio of area = 9×2/4 : x2 = 9:4

If the length of a rectangle is increased by 20% and it’s breadth is decreased by 20% then it area________?

by
If the length of a rectangle is increased by 20% and it’s breadth is decreased by 20% then it area________?

A. Increased by 4%
B. decreased by 4%
C. Decreased by 1%
D. Remains unchanged

Explanation:
Let length = x metres and breadth = y metres, then area =(xy)
New length =(120/100x)m = 6x/5 m
New breadth =(80/100 y)m
New area =(6x/5 x 4y/5)m2 = (24/25 xy)m2
Decreased in area =(xy – 24/25 xy)m2= xy/25 m2
Decreased % =(xy/25 x 1/xy x 100)% = 4%

If the length and width of a rectangular grand are each increased by 20% then what would be the percent increase in the area of the garden?

by
If the length and width of a rectangular grand are each increased by 20% then what would be the percent increase in the area of the garden?

A. 20%
B. 24%
C. 36%
D. 44%

Let length = x metres and breadth = y metres , then area =(xy)m2
New length = 120/100x (6x/5)m
New breadth = 120/100 y = 6y/5m
New area (6x/5 x 6y/5)m2 = (36/25 xy)m2
Increase in area = (36/25xy – xy)m2 = (11/25 xy)m2
Increase % = (11/25 xy x 1/xy x 100)% = 44%

The length of a rectangular plot is increased by 25%. To keep it’s area uncharged the width of the plot should be___________?

by
The length of a rectangular plot is increased by 25%. To keep it’s area uncharged the width of the plot should be___________?

A. Kept unchanged
B. Increased by 25%
C. Increased by 20%
D. Reduced by 20%

Explanation:
Let the length be x metres and breadth be y metres
Then it’s area =(xy)m2
New length =(125/100 x)m =(5x/4)m.
Let the new breadth be 2 metres
Then xy 5x/4 x 2 => 2 = 4/5 y
Decreased in width =(y -4/5 y) = y/5 metres
Decreased % in width =(y/5 x 1/y x 100)% = 20%

The perimeter of a rectangle and square are 160m each. The area of the rectangle is less than that it’s square by 100cm meters. The less than that of the square by 100 sq.meters. the length of rectangle is___________?

by
The perimeter of a rectangle and square are 160m each. The area of the rectangle is less than that it’s square by 100cm meters. The less than that of the square by 100 sq.meters. the length of rectangle is___________?

A. 30m
B. 40m
C. 50m
D. 60m
Explanation:
Each side of the square = 160/4m =40 cm
2(l+b) = 160
=> (l+b) = 80 (40) 2 –lb = 100
=> lb =(1600 – 100) = 1500 (l-b) 2 = (l+b) 2 – 4lb
= (80) 2 -4 x 1500 =(6400 -6000) = 400 (l-b) = 20
Therefore, l+b = 80, l-b =20
=> 2l =100
=> l= 50m