Solve the following and Choose the correct answer.
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1. The area of a square is 729 cm sq. It's perimeter are:
(1) 24 cm, 187 cm
(ii) 27 cm, 108 cm
(iii) 32 cm, 180 cm
(iv) 31 cm, 185 cm
2. The perimeter of a square is numerically equal to its area. Its area is:
(¡) 25 sq. units
(ii) 36 sq. units
(iii) 16 sq. units
(iv) 30 sq. units.
3. If each side of a rectangle is tripled, then the ratio of the perimeter of the original rectangle and the resulting
rectangle would be:
(1) 2:3
(ii) 4:5
(iii) 3:7
(iv) 1:3
4. If each side of a rectangle is doubled, then the ratio of the areas of the original rectangle and the resulting rectangle would be:
(i) 1:2
(ii) 1:4
(iii) 1:7
(¡v )1;8
5. The area of an equilateral triangle is 441√3cm², it's perimeter will be :
(1) 126 cm
(ii) 132 cm
(iii) 120 cm
(¡v) 142cm
6. The area of a right angled triangle with hypotenuse 50 cm and the other side as 26cm, will be:
(¡)555.50 cm²
(ii) 455.50 cm²
(iii) 565.50 cm²
(¡v) 555.21 cm²
7.A path of uniform width 3.5 m runs around the outside of a square of side of 21.5m.Area of the path will be:
(1) 160 m²
(ii) 162.75 m²
(iii) 350 m²
(¡v) 340m²
8. The radius of a circular wheel is 21 cm. Its area and perimeter will be:
(i) 2819 cm², 148 cm
(¡¡)1386m²,132cm
(¡¡¡) 1876 cm², 119 cm
(iv) 2167 cm²,142 cm
9. If the two parallel sides of a trapezium are 16 cm and 30 cm and perpendicular distance between them is 20cm, area of the trapezium will be:
(ii) 510 cm²
(iii) 460 cm²
(i) 490 cm²
(iv) 480 cm²
10. A square of side 7 cm is cut out of a rectangle of dimensions 11 cm by 13 cm,what will be the area of the left over rectangle?
(¡¡¡) 108 cm²
(ii) 94 cm²
(iv) 96 cm²
(i) 104 cm²
Answers
Answer:
1) solution:-
Area of square = 729 m^2
Area of square = (side)^2
( Side )^2 = 729
Side = √729
Side = √ 27 x 27
Side = 27 m
perimeter is =27X4=108
(ii)answer is correct
2)if perimeter of square is equals to it's area:-
perimeter =area of square
4×side=(side )^2
(4side)=(side)^2
side=4
hence,area is (4)^2
=>16squnit
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4) Let the sides of first rectangle be 'l' and 'b'. That implies second rectangle sides 2l and 2b.
Perimeter of original rectangle is 2(l+b) and resulting rectangle is 2(2l+2b).
Ratio of perimeter = 2(l+b)/ 4(l+b)
= 1/2 =1:2
Area of original rectangle is lb and resulting rectangle is 2l×2b.
Ratio of area = lb/ 4lb =1/4 =1:4
hope it helps you
please make it brainliest ☺️
1.
Let each side of the square be s cm
The area of the square is 729 cm²
We know that,
area of a square = side²
i.e., s² = 729
or, s² = 27²
or, s = 27 [ ∵ length cannot be negative, we take the positive value only ]
∴ each side of the square is 27 cm
∴ the perimeter of the square is
= 4s = 4 × 27 cm = 108 cm
OPTION (ii) is correct.
2.
Let each side of the square be s cm
By the given conditions, the numerical value of the perimeter of the square is equal to that of its area
i.e., 4s = s²
or, s² - 4s = 0
or, s (s - 4) = 0
or, s - 4 = 0 [ ∵ s ≠ 0 ]
or, s = 4
∴ each side of the square is 4 cm
∴ the area of the square is
= s² = 4² cm² = 16 cm²
OPTION (iii) is correct.
3.
Let the length and the breadth of the rectangle be l units and b units respectively
Then its perimeter is
= 2 (l + b) units
When the length and the breadth are tripled, the perimeter of the rectangle be
= 2 (3l + 3b) units
= 6 (l + b) units
∴ the ratio of perimeters is
= 2 (l + b) : 6 (l + b)
= 2 : 6 = 1 : 3
OPTION (iv) is correct.
4.
Let the length and the breadth of the rectangle be l units and b units respectively
Then its area is
= lb unit²
When the length and the breadth are doubled, the area of the rectangle be
= 2l × 2b unit²
= 4lb unit²
∴ the ratio of areas is
= lb : 4lb = 1 : 4
OPTION (ii) is correct.
5.
Let each side of the triangle be s cm
Then its area is = (√3/4) × s² cm^2
Given, √3/4 × s² = 441√3
or, s² = 4 × 441 = 2² × 21²
or, s = 2 × 21 = 42
∴ each side of the triangle is 42 cm
∴ the perimeter of the triangle is
= 3s = 3 × 42 cm = 126 cm
OPTION (i) is correct.
6.
Given, hypotenuse = 50 cm
& other side = 26 cm
∴ the other side be
= √(50² - 26²) cm
= √(2500 - 676) cm
= √1824 cm
= 4√114 cm
∴ the area of the right-angled triangle is
= 1/2 × 26 × 4√114 cm²
≈ 555.21 cm²
OPTION (iv) is correct.
7.
The area of the square of side 21.5 m is
= 21.5² m²
= 462.25 m²
and the area of the square with the path of 3.5 m is
= (21.5 + 3.5)² m²
= 25 m²
= 625 m²
∴ the area of the path is
= (625 - 462.25) m²
= 162.75 m²
OPTION (ii) is correct.
8.
The radius of the circular wheel is 21 cm
∴ its area is = π * 21 cm²
= 22/7 * 21 cm²
= 1386 cm²
& its perimeter is = 2π * 21 cm
= 2 * 22/7 * 21 cm
= 132 cm
OPTION (ii) is correct.
9.
The required area of the trapezium is
= 1/2 * (sum of parallel sides) * distance between the parallel sides
= 1/2 * (16 + 30) * 20 cm²
= 1/2 * 46 * 20 cm²
= 460 cm²
OPTION (iii) is correct.
10.
Given that, the sides of the rectangle are 11 cm and 13 cm.
∴ its area is = 11 × 13 cm² = 143 cm²
Each side of the square cut is 7 cm
So its area is = 7² cm² = 49 cm²
∴ after the square cut, the required area left is
= area of the rectangle - area of the square
= (143 - 49) cm²
= 94 cm²
OPTION (ii) is correct.