Advertisements
Advertisements
Question
The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If the area of the rectangle is three times the area of the square; find the dimensions of each.
Advertisements
Solution
Let a be the length of the sides of the square.
According to the question,
2a x ( a + 6 ) = 3a2
2a2 + 12a = 3a2
a = 12
Hence sides of the square are 12 cm each and
Length of the rectangle = 2a = 24 cm.
Width of the rectangle = a + 6 = 18 cm.
APPEARS IN
RELATED QUESTIONS
The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles; find the area of the quadrilateral.
Calculate the area of quadrilateral ABCD, in which ∠ABD = 90°, triangle BCD is an equilateral triangle of side 24 cm and AD = 26 cm.
A wire when bent in the form of a square encloses an area of 484 m2. Find the largest area enclosed by the same wire when bent to from:
- An equilateral triangle.
- A rectangle of length 16 m.
A footpath of uniform width runs all around the outside of a rectangular field 30 m long and 24 m wide. If the path occupies an area of 360 m2, find its width.
The perimeter of a rhombus is 46 cm. If the height of the rhombus is 8 cm; find its area.
The perimeter of a rhombus is 52 cm. If one diagonal is 24 cm; find:
(i) The length of its other diagonal,
(ii) Its area.
A floor that measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 25 cm. Find the number of tiles required.
Further, if a carpet is laid on the floor so that a space of 1 m exists between its edges and the edges of the floor, what fraction of the floor is left uncovered?
A triangle and a parallelogram have the same base and the same area. If the side of the triangle is 26 cm, 28 cm, and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Find the area of a quadrilateral field whose sides are 12m, 9m, 18m and 21m respectively and the angle between the first two sides is a right angle. Take the value of `sqrt(6)` as 2.5.
Find the area of the quadrilateral whose vertices are at (– 9, 0), (– 8, 6), (– 1, – 2) and (– 6, – 3)
