Question
The length of a rectangle is 8 cm
more than its breadth. If the area of the rectangle is 192 cm², determine the perimeter of the rectangle.Solution
ATQ,
Let the breadth of the rectangle be 'x' cm. Then, the length of the rectangle will be 'x + 8' cm. According to the given conditions, x(x+8) = 192 Or, x2 + 8x − 192=0
Factoring the quadratic equation, x2 +16x − 8x − 192 = 0 Or, x(x+16) - 12(x+16) = 0 Or, (x-12)(x+16) = 0 So, x = 12 or x = −16 (not possible)
Breadth of the rectangle = 12 cm Length of the rectangle = 12 + 8 = 20 cm Perimeter of the rectangle = 2(12+20) = 2×32 = 64 cm
The perimeter of semicircle is 36 cm and the radius of the semicircle is equal to the height of a Cylinder whose volume is 198 cm 3 . then fi...
The breadth ‘b’ of a room is twice its height and half of its length. Find the length of the longest diagonal of the room
The boundary length (perimeter) of a semicircle is 72 m. Find the area of a full circle whose radius is thrice the radius of that semicircle.
In a triangle ABC, D, E and F are the mid-points of the sides BD, CA and AB, respectively. BE and DF intersect at X. DE and CF intersect at Y. Find XY = ?
A right circular cylinder having total surface area of 44352 cm2 is immersed in a vessel completely filled with water. If the height of the c...
- A square and a rectangle have equal perimeters. The rectangle has length 18 cm and breadth 10 cm. What is the circumference of a semicircle whose radius eq...
If the radius and height of a right circular cylinder are increased by 22% and 28%, respectively, what is the percentage increase in its volume? (Use π...
2[sin x – cos x]4 + 6[sin x + cos x]2 + 5[sin6 x + cos6 x]= ?
The radius and height of a right circular cone are in the ratio 3: 4. If its curved surface area (in cm²) is 240 π, then its volume (in cm³...
If the length of a rectangle is extended by 25% and its width is reduced by 20%, what is the percentage difference in the rectangle's area as a result o...
Relevant for Exams:
