Question

If the areas of the given pairs of shapes are equal, find the value of x.​

Answer 1

X= 8cm

Explanation:

area of the square = s×s = 16×16 = 256cm

area of the rectangle = l×b = 32×x = 32x

Given , area of triangle = area of square

32x = 256

x= 256/32

x= 8cm

Answer 2

`x = 8cm`

Explanation:

we are given a square and rectangle.we want to figure out x which is the width of the rectangle. we are also given a condition i.e

• the area of the square equal to the area of the rectangle

therefore,

`\displaystyle \rm A _(square ) = A _(rect)`

recall the formula of the area of square and rectangle so,

`\displaystyle {s}^(2) = lw`

now assign variables

• 
  `s \implies16cm`
• 
  `l \implies32cm`
• 
  `w \implies x`

thus substitute:

`\displaystyle 32cmx = {16cm}^(2)`

simplify square:

`\displaystyle 32cmx = 256cm^2`

divide both sides by 32:

`\displaystyle \boxed{x = 8cm}`

and we're done!