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

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 = √(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 * 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 * 12`

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

Therefore :

▪︎The total cost of wire = Rs.11,232