Question

A brass tray in the shape of a parallelogram was polished at a total cost of Rs. 2250 at the rate of Rs. 20 per $$10c{m}^2$$.If the altitude of the parallelogram is 45 cm find the length of its base.

Answer 1

Hint: The shape given here is a parallelogram in form of a tray, try to figure out the area of the tray, by the help of the data given. Then apply the appropriate formula to find the length of its base.

Complete step by step solution:By the above assumption, we can easily assume that the area that was polished was accurately the area of the area of the parallelogram.
So, we are given that total cost of polishing the brass tray was $$=Rs.2250$$
We are also given the rate at which the brass tray was polished$$={\displaystyle \frac{Rs.20}{10c{m}^2}}$$
Let the area of tray be x.
So, Rs. 20 are spent for $$10c{m}^2$$ to be polished.
Rs. 2250 will be spent for x $$c{m}^2$$ to be polished.
By unitary method, we get,
For 1$$c{m}^2$$, the cost is Rs. 2
So, for $$xc{m}^2={\displaystyle \frac{2250}{2}}=1125c{m}^2$$
Step 2: From the above calculation we get that the area of the parallelogram is 1125$$c{m}^2$$
Now, let, the length of the base be L cm
& the length of altitude of the parallelogram be Alt. (i.e. 45cm)
So, we know that,
Area of Parallelogram$$=L\times Alt.$$
Or $$L={\displaystyle \frac{Area}{Alt.}}$$ ……………..(1)
So we got area of parallelogram as 1125$$c{m}^2$$
Altitude=45cm
Step 3: Putting the values in equation (1), we get,
$$L={\displaystyle \frac{1125}{45}}=25cm$$
So we got the length of the base as 25cm.

Note: It is important to keep an eye on the units given & convert them accordingly as the solution proceeds. Like instead of all being the same units (i.e. cm), the question could have the rate of 1 inch per 20Rs. or such. So, it is advised to the student to learn such conversion.