Question

The value for the area A of each figure is given. Write and solve a compound inequality for the value of x in each figure.

Help me plz.

Answer 1

`25.\\A=5\cdot x=5x\\\\35\geq5x\geq25\ \ \ \ |:5\\\\7\geq x\geq5\\\\26.\\A=(3\cdot x)/(2)=(3)/(2)x\\\\9\leq(3)/(2)x\leq12\ \ \ |\cdot(2)/(3)\\\\3\cdot2\leq x\leq4\cdot2\\\\6\leq x\leq8`

Answer 2

Length of Rectangle =x units

Breadth of Rectangle= 5 units

Area of Rectangle=Length × Breadth

=5x square units

It is given that , Area lies between 25 and 35.

⇒25≤ 5x ≤ 35

Dividing , the whole Inequality by 5, we get

⇒ 5 ≤ x≤7

⇒Part B

Area of Right Triangle

`=(1)/(2)* \text{Base} * \text{Height}\\\\=(1)/(2)* 3 * x\\\\=(3x)/(2)\\\\\rightarrow 9\leq (3x)/(2)\leq 12\\\\ \text{Multiplying whole inequality by ,2}\\\\\rightarrow18\leq 3x \leq 24\\\\\text{Dividing whole inequality by ,3}\\\\\rightarrow 6\leq x \leq 8`

⇒6≤x≤8