Question
The diagonal of a rectangular plot is $34 \ m$ and its perimeter is $92 \ m$. Find its area.
✓
Answer
Let a and $b$ be the sides of the rectangle
Since the perimeter is $92\ m$, we have,
$2( a + b ) = 92$
$\Rightarrow a + b = 46\ m ...(1)$
Also, given that diagonal of a trapezium is $34\ m.$
$\Rightarrow a^2 + b^2 = 34^2....(2)$
We know that
$( a + b )^2 - a^2 - b^2 = 2ab$
From equations $(1)$ and $(2)$, we have,
$46^2 - 34^2 = 2ab$
$\Rightarrow 2ab = 960$
$\Rightarrow ab=\frac{960}{2}$
$\Rightarrow ab = 480\ m^2.$
Since the perimeter is $92\ m$, we have,
$2( a + b ) = 92$
$\Rightarrow a + b = 46\ m ...(1)$
Also, given that diagonal of a trapezium is $34\ m.$
$\Rightarrow a^2 + b^2 = 34^2....(2)$
We know that
$( a + b )^2 - a^2 - b^2 = 2ab$
From equations $(1)$ and $(2)$, we have,
$46^2 - 34^2 = 2ab$
$\Rightarrow 2ab = 960$
$\Rightarrow ab=\frac{960}{2}$
$\Rightarrow ab = 480\ m^2.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Mr Goyal bought a car for ₹ 6,25,000. Its value depreciates at 20% p.a. How many years it would take for the price of the car to go down by ₹3,69,000?
For solving pair of equation, in this exercise use the method of elimination by equating coefficients $:13 + 2y = 9x,3y = 7x$
→Given: $\text{ED} = \text{EC}$, Prove: $\text{AB}+\text{AD}>\text{BC}$.
→If the following pair of the triangle is congruent? state the condition of congruency:In $\triangle ABC$ and $\triangle PQR, \text{AB} = \text{PQ}, \text{AB} = \text{PQ},$ and $\text{BC} = \text{QR}.$
→Check whether the following statement is true or false. Justify your answer. If the length of an are of a circle of radius is equal to that of an arc of a circle of radius 2r, then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle.
Show that the bisectors of the angles of a parallelogram enclose a rectangle.
If $(a+b)=2$ and $(a-b)=10$, find the values of : $\left(a^2+b^2\right)$
→The circumference of a circle exceeds its diameter by 180 cm. Calculate (i) the radius (ii) the circumference and (iii) the area of the circle.
[Hint. $(2 \pi r-2 r)=180$.]
→[Hint. $(2 \pi r-2 r)=180$.]
Plot the points $A (3, 4)$ and $C (-3, -2)$ on a graph. Find the coordinates of the point $B$ and $D$ such $\text{ABCD}$ is a square. Also find the area of the square.
→Factorise : $4x^4- x^2- 12x - 36$
→