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 origin…

Question

asked Jul 22, 2020 41.9k views

1 Answer

Drauka · Answer 1 · 2020-07-28T02:42:36+0000

Answer:

10

Explanation:

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

To Find: If area is
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
$=\text{length of one side}*\text{length of other side}$

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

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

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