Question

22
A plot of land is in the shape of a right-angled triangle whose
base and perpendicular are 65m and 72m respectively. If its
boundary is made by using 4 round iron wire, find the total cost of
the wire at the rate of Rs. 12 per meter. (Ans: Rs. 11,232)​

Answer 1

Answer:

65^2 + 72^2 = hypotenuse^2 = 9409

hypotenuse = 97

65 + 72 + 97 = 234 m perimeter

234 x 12 = 2808 cost per one row

2808 x 4 = 11,232 cost per 4 rows

Answer 2

Given :

▪︎A plot of land is in the shape of a right angled triangle.

▪︎Length of base of triangle = 65 m

▪︎Length of perpendicular of the triangle = 72 m

We know that :

$\color{hotpink} \tt {hypotenuse}^{2} \color{plum}= {height}^{2} + {base}^{2}$

The hypotenuse or length of the third side :

$= \tt{h}^{2} = {65}^{2} + {72}^{2}$

$= \tt {h}^{2} = 4225 + 5184$

$= \tt {h}^{2} = 9409$

$=\tt h = \sqrt{9409}$

$\hookrightarrow \tt \color{plum}h = 97 \: m$

Thus, the length of the hypotenuse of the plot = 97 m

Perimeter of the plot :

$=\tt side + side + side$

$= \tt65 + 72 + 97$

$\color{plum}=\tt 234 \: m$

Thus, the perimeter of the plot = 234 m

Boundary of the plot is made by = 4 wires

Length of wire needed :

$=\tt 234 \times 4$

$\color{plum} =\tt 936 \: m$

Thus, quantity of wire needed = 936 m

Cost of 1 m of wire = Rs.12

Cost of 936 m of wire :

$= \tt936 \times 12$

$\color{plum}=\tt\bold{Rs. \: 11232}$

Therefore :

▪︎The total cost of wire = Rs.11,232