Question
The perimeter of a square field is 10 cm more than the
perimeter of a rectangle. The length of the rectangle is 60 cm which is 80% of its width. If a street of width 10 cm surrounds from outside the square, then find the total cost of constructing the street at the rate of Rs. 20 per sq. cm.Solution
Let the width of the rectangle = x cm Then, 80% of x = 60 x = 60 × 100/80 = 75 cm Perimeter of the rectangle = 2 (length + width) = 2 × (60 + 75) = 270 cm Perimeter of the square = (270 + 10) = 280 cm The sides of the square = 280/4 = 70 cm The area of the square field without street = (70)2 sq. cm = 4900 sq. cm  The area of the square field with street = (70 + 20)2 sq. cm = 8100 sq. cm The area of the street = 8100 – 4900 = 3200 sq. cm The total cost of constructing the street = 3200 × 20 = Rs. 64000
- Find the distance between the parallel sides of a trapezium whose area is 315 cm² and the lengths of the parallel sides are 15 cm and 21 cm respectively.
A triangle has sides 13 cm, 14 cm, and 15 cm. Find the area of the triangle.
In triangle ABC, AB = 8 cm, AC = 6 cm and BC = 10 cm. The bisector of angle A meets side BC at point D. What is the length of BD (in cm)?
Find area of a trapezium with parallel sides 12 cm and 18 cm, height 10 cm.
In a right-angled triangle, the hypotenuse is 20 cm, and one of the legs is 12 cm. Find the area of the triangle.
The altitude of an equilateral triangle is 6√3 cm. Find the area of the equilateral triangle.
If two triangles XYZ and ABC are congruent, then which of the following statement(s) is/are true?
I. XY = AB
II. ∠X = ∠A
- Calculate the area of a triangle whose base is 19.5 cm and the height corresponding to it is 13.7 cm.
If perpendicular and base of a right-angle triangle is, 18 cm and 24 cm, respectively, then find the length of the shortest median of triangle.
The ratio of the height to the base of a triangle is 3:2. If the sum of the height and base of the triangle is 25 cm, what is the area of the triangle?
Relevant for Exams:
