Question

Given the diagram below, if the area of the shaded region is 103 ft2, what are the dimensions of the inside triangle?

Answer 1

Bigger rectangle:

we can see that

length is 3x-2

so, $L=3x-2$

width is x+6

so, $W=x+6$

now, we can find area

$A_b=L\times W$

$A_b=(3x-2)\times (x+6)$

Smaller rectangle:

we can see that

length is 2x

so, $L=2x$

width is x-1

so, $W=x-1$

now, we can find area

$A_s=L\times W$

$A_s=(2x)\times (x-1)$

Area of shaded region:

Area of shaded region = area of bigger rectangle - area of smaller rectangle

$A=A_b-A_s$

we can plug values

$A=((3x-2)\times (x+6))-((2x)\times (x-1))$

we are given that area as 103 ft^2

so, we can set it equal

$103=((3x-2)\times (x+6))-((2x)\times (x-1))$

now, we can solve for x

$103=x^2+18x-12$

$x^2+18x-12-103=103-103$

$x^2+18x-115=0$

now, we can factor it

$(x-5)(x+23)=0$

$x=5,x=-23$

Since, length can never be negative

so,

$x=5$

now, we can find dimensions of inner rectangle

Length is

$L=2\times 5$

$L=10ft$

width is

$W=5-1$

$W=4ft$

so, dimensions are

$L=10ft$

$W=4ft$..............Answer