Question

10. The dimensions of a rectangle were originally 10 units by 12 units. The

area of the rectangle increased by 135 square units, and the dimensions were increased
by the same amount. Find the dimensions of the new rectangle.

Answer 1

Length=17 units

Width=15 units

Explanation:

Let x be the magnitude by which the dimensions increase. And 135 sq units the magnitude by which the area increased:

`A=lw\\\\(10+x)(12+x)=120+135\\\\120+22x+x^2=255\\\\x^2+22x-135=0\\\\x^2+27x-5x-135=0\\\\(x-5)(x+27)=0\\\\\#Take \ +ve \ root\\\\x=5`

We add the value of x to the old dimensions to find the new dimensions:

length=12+x=12+5=17 units

Width=10+x=10+5=15 units