**Equations in single variable based on area and perimeter of quadrilaterals in geometry are given here. Our special focus is area and perimeter of triangles, trapezoids, parallelograms, rectangles and hexagons. Few questions are based properties of angles in a triangle.**

**1.**

**A rectangular cupboard is of length 6m and perimeter 20 m. Find the width of the cupboard.**

__Solution:__**Length of cupboard, l = 6m**

**Perimeter of cupboard= 20m**

**Width of cupboard =w**

**Perimeter of rectangle=2*(l + w)**

**2(l + w) =20**

**2(6 + w) = 20**

**Dividing by 2 on both sides,**

**6+w = 10**

**Subtracting 6 on both sides,**

**W =4**

**Therefore, width of rectangular cupboard is 4 m.**

**2.**

**The sides of scalene triangle are in the ratio 2:4:3 and its perimeter are 27 inches. Find the sides of the triangle.**

__Solution:__**Let 2x, 4x and 3x are the sides of the triangle.**

**Perimeter= 27 inches**

**So, 2x + 4x + 3x = 27**

**9x =27**

**Dividing by 9 on both sides,**

**X=3**

**The sides of the triangle are 2*3, 4*3 and 3*3**

**Therefore, the sides of the triangle are 6 inches, 12 inches and 9 inches.**

**3.**

**The area of trapezium is 84 Sq.cm and height is 8 cm. The parallel sides are in the ratio 2: 5. Find the length of the bases.**

__Solution:__**Area of trapezium = 84 Sq.cm**

**Height of trapezium=8 cm**

**Let the parallel sides be 2x and 5x**

**Area of trapezium = 1/2 *height*(base 1+base 2)**

**84=1/2 *8*(2x+5x)**

**84= 4*7x**

**Dividing by 28 on both sides,**

**X=3**

**The parallel sides are 2*3 and 5*3**

**Therefore, the parallel sides are 6 cm and 15 cm.**

**4.**

**The perimeter of an equilateral triangle is 54 cm. Find the length of each side of triangle.**

**5.**

**Mr. White purchased a carpet for rectangular hall of area 800 sq. yards. The length of the hall is 32 yards. Find the required width of the carpet.**

**6.**

**The area of right angled triangle is 32. If the base is 8 cm, find its height.**

**7.**

**The length of the rectangular building is 7 ft more than its width. If the perimeter of the building wall is 98 ft, find its length and width.**

**8.**

**The area of a rectangular garden is 1800 sq. ft. Find the width if its height measures 40 ft.**

**9.**

**The perimeter of a hexagonal display board is 42 cm. The board has to be bordered around with satin ribbon. Find the length of ribbon required to border each side.**

**10.**

**In an isosceles triangle one of the angles of a triangle is 54 degrees. Find the base angles of the triangle.**

**11.**

**The zee Theme Park’s fountain wall is in the shape of equilateral triangle. The total perimeter of the wall is 51 yards. Find the measure of each side of the wall.**

**12.**

**A rectangular swimming pool was constructed for Kids at Hotel Park. The length of the swimming pool is twice its width. If the length is 16 ft, find the width and area of the pool.**

**13.**

**The base of the parallelogram is 11 inches and its area is 132 Sq. inches. Find the height of the parallelogram.**

**14.**

**The angles of a triangle are in the ratio 1:2:3. Find each angle of the triangle.**

**15.**

**Find the angles of the triangle if the second angle is 32 degree less than thrice the first angle and the third angle is 28 degree less than twice the first angle.**

**16.**

**The perimeter of two squares ABCD and PQRS are 3:2 respectively. The sums of the perimeters of the squares are 30. Find the perimeter of ABCD and PQRS.**

**17.**

**A field is in the shape of an equilateral triangle attached to the width of the rectangular region where width of the rectangle and side of the triangle measures the same. The length of rectangular region is 76 ft and the side of triangular region measures 42 ft. Find the perimeter of the field.**

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