Question

the rectangle below is dilated by a scale factor of 4. find the perimeter and area of the rectangle below, as well as the perimeter and area of the dilated rectangle. express your answers as whole numbers, decimals, or fractions in simplest terms (no mixed numbers). figures are not necessarily drawn to scale. answer perimeter of given rectangle units area of given rectangle units² perimeter of dilated rectangle units area of dilated rectangle units²

Explanation:

Step1: Calculate perimeter of given rectangle

The formula for the perimeter of a rectangle is $P = 2(l + w)$, where $l = 11$ and $w = 8$. So $P=2(11 + 8)=2\times19 = 38$ units.

Step2: Calculate area of given rectangle

The formula for the area of a rectangle is $A=l\times w$. So $A = 11\times8=88$ square - units.

Step3: Find new dimensions after dilation

When a rectangle is dilated by a scale factor of $k = 4$, the new length $l_{new}=11\times4 = 44$ and the new width $w_{new}=8\times4 = 32$.

Step4: Calculate perimeter of dilated rectangle

Using the perimeter formula $P_{new}=2(l_{new}+w_{new})$, we have $P_{new}=2(44 + 32)=2\times76 = 152$ units.

Step5: Calculate area of dilated rectangle

Using the area formula $A_{new}=l_{new}\times w_{new}$, we get $A_{new}=44\times32 = 1408$ square - units.

Answer:

Perimeter of given rectangle: 38 units
Area of given rectangle: 88 units²
Perimeter of dilated rectangle: 152 units
Area of dilated rectangle: 1408 units²