Question

A rhombus sheet, whose perimeter is 32 m and whose one diagonal is 10 m long, is painted on both sides at the rate of ` 5 per m2. Find the cost of painting.

• A. Rs. 630
• B. Rs. 625
• C. Rs. 312.24
• D. Rs. 62.44

Answer 1

The correct option is B Rs. 625

Perimeter = 32 m,
So, length of a side =32/4=8m,
and Diagonal of a rhombus = 10m,
As, we know that,
The halves of diagonals and a side of a rhombus from a right angled triangle with side as hypotenuse.
Let the length of the other diagonal =2x.
$x^2+(10/2{)}^2=8^2=x^2+25=64$
$x^2=64-25=39$
$x=\sqrt{39}$
The measure of the another diagonal of the rhombus = 2*\sqrt { 39 } =2\sqrt { 39 } m
So, Area of the rhombus =1/2*Diagonal of a rhombus*Measure of the another diagonal
$A=\frac{1}{2}\times 10\times 2\sqrt{39}$
$A=62.45m^2$
painted on both sides at the rate of Rs 5 per m2
Cost = area of both side*5=2*62.45*5=624.50 Rs

Answer (B) Rs. 625