Question

If the length of one side of a square is triple and the length of an adjacent side is increased by 10, the resulting rectangle has an area that is 6 times the area of the original square. Find the length of a side pf the original square.

Answer 1

Answer:

10

Step-by-step explanation:

Given: If the length of one side of a square is triple and the length of an adjacent side is increased by $10$.

To Find: If area is $6$ times the area of original square find length of a side of original square.

Solution:

Let the side of original square be $=\text{x}$

area of original square $=\text{x}^2$

when length of side is tripled,

new length of one side of square $=3\text{x}$

length of other side is increased by 10 unit

new length of other side of square $=\text{x}+10$

new area of resulting rectangle $=\text{length of one side}\times\text{length of other side}$

                    $=(\text{x}+10)\times(3\text{x})$

                    $3\text{x}^{2}+30$

As area of resulting rectangle is 6 times the original square

           $3\text{x}^{2}+30=6\text{x}^2$

           $3\text{x}^2-30=0$

           $3\text{x}(\text{x}-10)=0$

           $\text{x}=10,0$

as length cannot be zero

           $\text{x}=10$

Hence the length of a side of original square is $10$