Question

Area of a rectangle whose length is greater than breadth is given by $25a^2-35a+12.$ Match the following when $a=4.$

• A. 272 sq units
• B. 16 units
• C. 66 units
• D. 17 units

Answer 1

Here, area is given in terms of a quadratic expression in one varaible. To find the possible length and breadth of a rectangle, we have to factorise the given expression.

$Area=25a^2-35a+12(Area=l\times b)=25a^2-20a-15a+12\left(splittingmiddleterm\right)=5a(5a-4)-3(5a-4)=(5a-4)(5a-3)$

Since Length is greater than breadth, $5a-3$ is the length and $5a-4$ is the breadth.

When $a=4,$
Length $=5a-3=5\left(4\right)-3=17$
Breadth $=5a-4=5\left(4\right)-4=16$
Perimeter $=2\left(\right(5a-3)+(5a-4\left)\right)=2(17+16)=66\text{units}$
Area $=(5a-3)(5a-4)=17\times 16=272\text{sq units.}$