Advertisements
Advertisements
Question
The diagonal of a rectangular plot is 34 m and its perimeter is 92 m. Find its area.
Solution
Let a and b be the sides of the rectangle
Since the perimeter is 92 m, we have,
2( a + b ) = 92
⇒ a + b = 46 m ...(1)
Also, given that diagonal of a trapezium is 34 m.
⇒ a2 + b2 = 342 ....(2)
We know that
( a + b )2 - a2 - b2 = 2ab
From equations (1) and (2), we have,
462 - 342 = 2ab
⇒ 2ab = 960
⇒ ab = `960/2`
⇒ ab = 480m2.
APPEARS IN
RELATED QUESTIONS
The perimeter of a rectangular board is 70 cm. Taking its length as x cm, find its width in terms of x.
If the area of the rectangular board is 300 cm2; find its dimensions.
Trapezium given below; find its area.
Trapezium given below; find its area.
Calculate the area of the figure given below: which is not drawn scale.
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.
The floor of a room is of size 6 m x 5 m. Find the cost of covering the floor of the room with 50 cm wide carpet at the rate of Rs.24.50 per metre. Also, find the cost of carpeting the same hall if the carpet, 60 cm, wide, is at the rate of Rs.26 per metre.
In the following, find the value of ‘a’ for which the given points are collinear
(2, 3), (4, a) and (6, – 3)
In the following, find the value of ‘a’ for which the given points are collinear
(a, 2 – 2a), (– a + 1, 2a) and (– 4 – a, 6 – 2a)
Find the area of the quadrilateral whose vertices are at (– 9, – 2), (– 8, – 4), (2, 2) and (1, – 3)
PQRS is a rectangle formed by joining the points P(– 1, – 1), Q(– 1, 4), R(5, 4) and S(5, – 1). A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer.
