Question

Please help answer the two questions in the photo

Answer 1

The given pentagon can be divided into two figures : a triangle and rectangle as shown in figure.

Let us find area of each figure separately.

Triangle:

Area of triangle is given by:

$A=\frac{1}{2}*b*h$

where b=base and h=height

Height of triangle :

h=(3x+5)-(2x+1)

h=x+4

Base = 2x-2

$A=\frac{1}{2}*(x+4)(2x-2)$

Area of triangle= (x-1)(x+4) = x²+3x-4

Area of rectangle:

Area of rectangle is given by:

A=l*b

$A=(2x-2)(2x+1)$

Area of rectangle = 4x²-2x-2

Area of pentagon = Area of triangle + Area of rectangle

Area of pentagon = x²+3x-4 + 4x²-2x-2

Area of pentagon = 5x²+x-6

If area of pentagon is 42 cm², then solving for x,

$42=5x^{2}+x-6$

$5x^{2}+x-48=0$

Factorising to get x,

x=-3.2 and x=3

If we take x as negative the side will be negative, so we neglect x=-3.2

So x=3 is the answer.